Gary Allen Steele fired a gun near his former girlfriend during an argument. Donald Snider harassed a minor. Claudia Wright faced forgery charges. Frank Garcia was accused of shooting out his window while driving drunk.

All pleaded guilty to crimes or left jobs to avoid prosecution. All were police officers at the time of their alleged misconduct. All still are.

They are among hundreds of officers in America who still have badges after being charged with crimes, The Wall Street Journal found in an examination tracking outcomes of police-misconduct cases across every state.

Infractions that can disqualify barbers, child-care providers and others needing state certification don’t necessarily bar officers from retaining jobs or getting new ones. In America’s patchwork system, most states let some officers remain on the force despite misconduct, including actions that other states might consider disqualifying.

And while states routinely have databases letting citizens check the licensing status of, say, an auctioneer, many states don’t readily offer such listings of police, and some refuse to make public even the names of officers.

The Journal’s analysis gives credence to the notion put forth by some law-enforcement officials that police misconduct—which has become a point of national debate after a series of high-profile shooting deaths, some on video—might in part stem from the presence of a small but persistent minority of “bad apple” officers who are allowed to stay on the job.

It is frequently possible for problem officers to keep their posts or move from job to job, the analysis shows. Some police agencies don’t always check whether applicants have records of misdeeds. Among states with processes for stripping officers of certification, some didn’t decertify a single one in 2015. Union rules often help officers retain their jobs.

Police officials acknowledge standards should be high given the life-or-death authority vested in officers. While all accused officers deserve due-process rights, that shouldn’t be a barrier against holding them accountable for severe misconduct, said Los Angeles County Sheriff Jim McDonnell. Discharging problem officers “is a challenge for police chiefs and sheriffs across America,” he said “because the review process will sometimes uphold the findings of misconduct, but reduce the penalty of termination to suspension days.”

The Journal traced outcomes for 3,458 police officers from across the U.S. whose arrests resulted in their losing jobs or being convicted—or both—in the seven years through 2011. The information about the arrests was compiled from news reports by Bowling Green State University criminologist Philip Stinson, who holds some of the most detailed U.S. data on police misconduct.

To track what happened to each officer, the Journal reviewed police-officer listings, employment histories and other records from all 50 states, sometimes using public-record-act requests. The Journal found that 1,927 who left their departments after brushes with the law weren’t in law enforcement in 2015 but had not been placed on any list of decertified officers, which would create a formal prohibition to their returning to the profession in their states. Of the remainder, 430 were imprisoned, including 261 who hadn’t been decertified. Another 738 were decertified but not incarcerated, and 31 had died.

Almost 10%, 332 of the officers, remained in law enforcement. Some officers stayed in the profession after convictions for killing or injuring people through negligence or recklessness, or for drunken-driving infractions. Others were convicted of crimes such as beatings, brandishing weapons illegally, stealing or lying.

In a few cases, convictions were overturned on appeal, though many underlying facts of the misconduct weren’t generally in dispute.

A felony conviction—such as rape or assault with a deadly weapon—almost always ejects an officer from the profession. Officers can survive misdemeanors, however, in states such as Michigan, where Gary Allen Steele of the Detroit Police Department was arrested in March 2008 after a fight with his former girlfriend.

Police reports alleged he hit her with a bat, pinned her down, fired three shots near her head and put the gun into her mouth while screaming he would kill her, before releasing her.

Mr. Steele acknowledged firing the gun, police reports show. Wayne County, Mich., prosecutors charged him with torture, assault with intent to murder and other felonies. The department suspended him. In 2009, he was back on the job after pleading no contest to reckless firearm discharge, a misdemeanor which, in Michigan, doesn’t disqualify an officer.

Mr. Steele might not have stayed working in at least five states—Maine, Missouri, New Mexico, Oregon, West Virginia—where a misdemeanor is grounds for revoking certification. Forty-five states require such a certification, which can include training and background checks, said the International Association of Directors of Law Enforcement Standards and Training. This professional organization maintains a database of decertified officers available to police agencies, but reporting can be spotty.

Richard Convertino, Mr. Steele’s attorney, said prosecutors “exponentially overcharged” his client “with crimes he didn’t even remotely commit.” He said the former girlfriend was the aggressor and Mr. Steele fired to stop her.

Detroit Police spokesman Michael Woody said Mr. Steele was suspended when he was charged. Even after that was resolved, he said, the officer continued serving a “lengthy suspension period” because an internal investigation determined he violated department policy “in a number of areas.” Wayne County prosecutor’s office spokeswoman Maria Miller declined to comment. A court clerk said the case files were sealed.

File sealing, which the Journal found in other cases, makes it hard for potential employers and citizens to research an officer’s past. And arbitration panels can limit ability to discharge an officer, say police officials.

Officer Donald Snider, 54, of the Pittsburgh police was charged in 1999 with indecent assault against a 16-year-old girl and corrupting the morals of a minor. The department fired him, rehiring him after he pleaded no contest to a summary charge of harassment, court documents show.

Mr. Snider might not have kept his job if he were a cosmetologist, one of 29 professions licensed by Pennsylvania. The state cosmetology board would have considered revocation or other discipline for a cosmetologist accused of the same thing, said a lawyer for the board.

Mr. Snider was fired again when internal investigators concluded he unlawfully arrested a man and lied about the man’s swallowing heroin, arbitration documents show. He was arrested at an arbitration hearing in January 2005, accused of trying to bribe the man to change his testimony. He was found not guilty of criminal solicitation and criminal conspiracy. Arbitrators decided he had reasonable suspicion for the arrest and there wasn’t enough evidence to show he lied. He got his job back.

Mr. Snider’s attorney, Bryan Campbell, said his client declined to comment and his legal record shouldn’t disqualify him from being an officer. “The question gets to be, does every criminal matter merit a termination?” said Mr. Campbell. “I think it’s gotta be something fairly serious.” The Pittsburgh Bureau of Police declined to comment.

Mr. Snider works in one of many states that strip certification from very few officers. Pennsylvania has reported no officer decertifications since 2012 and just 31 in the past 12 years, according to data the state provided to the Journal. Cpl. Adam Reed, a spokesman for the Pennsylvania agency in charge of decertification, said the state’s law is “very specific” as to when an officer can be decertified and the agency “does not act as an ‘internal affairs.’ ”

There are striking disparities in how often states decertify. Georgia provided the Journal a list of 5,624 officers decertified from 2004 to 2015. Louisiana reported nine decertifications over that same time frame. Bob Wertz, who works for the Louisiana state council that handles decertifications, said the local departments must start the process by reporting the matter.

“We are just floored” when hearing about states that decertify just a few, said Ryan Powell, director of operations at the Georgia Peace Officer Standards and Training Council. “Officers in other states are doing the same things we discipline them for here.”

Problem officers make things difficult for good ones, said Jim Pasco, executive director of the Fraternal Order of Police, America’s largest police-labor organization. “If you find an officer has committed an egregious wrong” and due process is followed, he said, “that officer should be decertified.”

New state, new badge

Losing her badge didn’t keep Claudia Wright from getting a new one in another state. In 2011, the Daytona Beach police officer relinquished her certification in Florida in a plea deal to resolve forgery and identity-theft charges.

Police investigative documents said she allegedly forged her grandmother’s signature to buy a car and she agreed to forfeit her certification as part of felony charges being dropped. The agreement said the relinquishment was “permanent with no opportunity for reinstatement.”

She is now certified in Virginia, working at the Richmond City Sheriff’s Office. Florida failed to send information concerning her to the decertification database. After a Journal inquiry, Ms. Wright’s decertification action was submitted. Gretl Plessinger, spokeswoman for the Florida Department of Law Enforcement, said the officer’s name should have been forwarded to the database.

Virginia law doesn’t prevent a local police department from hiring an officer decertified in another state. A Richmond-sheriff spokesman declined to comment. Virginia state officials said it is up to local agencies to do background checks. Ms. Wright said she hadn’t been convicted of a crime, declining to discuss her employment.

Some states don’t have a decertification process, including California and New Jersey, where hiring and firing is left to departments. Frank Garcia was a Huntington Park, Calif., officer when arrested in 2003 and charged with a misdemeanor for driving drunk and a felony for firing his service revolver out the window, court documents show. He pleaded guilty to a misdemeanor of discharging a firearm from a public roadway and resigned.

In neighboring Arizona or Oregon, the arrest and plea would have been grounds for decertification proceedings, officials in those states said. A decertification in either state is permanent.

A year later, a judge let Mr. Garcia withdraw his plea. Nearby Maywood police department hired him. There, Mr. Garcia was a defendant with two other officers in a suit alleging they mistreated a mentally handicapped woman. It was settled for $18,000 without admission of wrongdoing.

The Maywood department disbanded in 2010 after California’s attorney general found it was riddled with excessive-force and sexual-misconduct problems and had a reputation as an “agency of last resort” for troubled officers.

The Los Angeles County Sheriff’s Department in 2011 hired Mr. Garcia and other Maywood officers. The sheriff’s office of independent review later criticized its hiring procedures as lax, saying in a report that, when confronted with details of Mr. Garcia’s criminal case, the undersheriff “stated that he may not have hired the applicant given the specifics of the case.”

The watchdog agency faulted the department for paying attention only to the final disposition of Mr. Garcia’s criminal case and failing “to appreciate the troubling facts regarding the applicant’s specific behavior and acts which were serious in nature.” The report didn’t name Mr. Garcia; people familiar with the inquiry said he was the applicant.

A Los Angeles County Sheriff spokeswoman declined to comment on why Mr. Garcia left the department.

Mr. Garcia began using the surname Huizar. In 2013, he was hired by California City, where he is a lieutenant. He said he would “rather not talk about” his past and that using the surname was “personal.”

His police chief, Eric Hurtado, in a written response said the department thoroughly reviewed Mr. Garcia, who listed both names when he applied for the job. He said tolerance has grown for blemishes on officers’ records.

“Right now, there is a vast shortage of ‘Perfect People’ who are willing to put on a bulletproof vest and have to carry a gun just to go to work,” said Mr. Hurtado. The chief has since gone on administrative leave for personal reasons, the city said. He didn’t respond to subsequent requests for comment.

Paying the price

Some police agencies, because of lack of money, can’t attract high-quality candidates and hire officers who couldn’t get jobs elsewhere, said David Harvey, executive director of Michigan’s Commission on Law Enforcement Standards. That may be part of why Inkster, Mich., hired William Melendez, said Mr. Harvey, who was previously the police chief in neighboring Garden City.

Mr. Melendez joined the nearly bankrupt town’s force in 2010 after about 15 years as a Detroit officer, where he was a defendant in at least a dozen civil lawsuits alleging excessive force, wrongful death and other misconduct, federal court documents show. Several were dropped and a few were settled without admission of wrongdoing, including a 1996 case in which Mr. Melendez and another officer allegedly fatally shot an unarmed motorist who was lying down. Detroit settled with the man’s family for more than $1 million.

In 2003, federal prosecutors in Detroit charged him with being part of a group of officers who conducted illegal searches, planted drugs, beat suspects and made arrests without probable cause, according to the indictment. Mr. Melendez was acquitted and retired.

His record didn’t prevent him under Michigan law from working in Inkster. Last year, cameras caught him dragging a man who ran a stop sign out of his car and beating him. He was convicted of assault and misconduct. Inkster settled with the victim for $1.4 million.

James Thomas, a lawyer for Mr. Melendez, who is appealing, said his client declined to comment, calling the 2003 indictment a “witch hunt.”

Gregory Gaskin, the former Inkster police chief who hired Mr. Melendez, didn’t respond to inquiries. In a recent deposition in a separate civil suit against Inkster and Mr. Melendez, Mr. Gaskin was asked about a pre-hiring background investigation of Mr. Melendez that noted the 2003 indictment. He answered: “Well, I read it, but as far as significance, I didn’t think much of it.”

Advocates for stronger reporting say records should follow officers systematically. Some urge focusing on misconduct, not just convictions.

A commission President Barack Obama created after the 2014 Michael Brown shooting in Ferguson, Mo., calls for the national decertification database to be expanded to all police agencies.

St. Louis University law-school professor emeritus Roger Goldman, among America’s pre-eminent experts on police, points out Congress has made such reporting mandatory in medicine, requiring data on practitioner’s malpractice payouts and disciplinary actions be sent to a central repository.

“With all the concern about bad cops,” he said, “you would figure the feds would have something similar for law enforcement.”

Write to Louise Radnofsky at [email protected], Zusha Elinson at [email protected], John R. Emshwiller at [email protected] and Gary Fields at [email protected]

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Judge Vonda Evans Sentences Former Police Officer William Melendez for Assault and Misconduct