A San Jose State cop fired in 2017 for beating a man in the library then reinstated over the university’s objections went to work in September for the Los Gatos-Monte Sereno Police Department. On Friday, after this news organization revealed his troubled past, he abruptly resigned.

An Alameda County deputy sheriff fired in 2015 for soliciting prostitution and dishonesty after he filed a false police report related to his divorce was later hired by the Pinole Police Department.

The two cases, recently disclosed under a new state law, raise serious questions about the revolving door for troubled cops and the hiring practices of California police departments that employ officers who have been canned elsewhere.

Not only might members of the communities have concerns about the police patrolling their streets, there’s another large question about whether the cops can be effective in their jobs — especially when called to testify in criminal cases.

Before this year, these cases probably would never have seen the light of day. But a new state law, created by last year’s approval of Senate Bill 1421, requires police agencies to release documents pertaining to cops’ discharge of firearms, use of major force, sexual assault and dishonesty.

As we noted earlier this month, the information in the records has been disturbing: Stolen drugs and bullets. A potentially deadly chokehold. Falsified reports. A person’s face smashed into the floor. Sexual assault in jail. Cavorting with sex workers. Domestic violence complaints against an officer ignored.

Equally disturbing is the police foot-dragging on release of the records. When it comes to transparency, a majority of the agencies across California responsible for enforcing the law are defying it.

Now come these two new cases that raise another key issue: The revolving door means that police departments are hiring cops who, because of their past behavior, cannot fully perform their jobs.

That’s because, under a 1963 U.S. Supreme Court ruling, Brady v. Maryland, prosecutors must disclose to defense attorneys any evidence that could help them defend their clients. That includes information about past dishonesty or other bad behavior of the cops involved in the case.

It’s only fair. After all, if an officer has been fired for lying or misconduct, it goes to the heart of his or her credibility. The jury should know about it. And, from a practical perspective, a cop who can’t testify can’t carry out a critical part of the job.

District attorney offices across the state keep “Brady lists” of officers who have been identified as potentially problematic witnesses. But they’re not always complete. And they can miss cops who were hired after past jobs in other counties.

The new state law should help, making available some of the same records to not only police agencies, prosecutors and defense attorneys, but also to the public. Not surprisingly, in Los Gatos and Monte Sereno, residents who saw the disturbing video of the San Jose State library beating were not happy that the cop was working in their city.

In that case, Officer Johnathon Silva was first cleared by the university’s police chief at the time, Peter Decena, who decided the use of force was not excessive. But after the beating victim, who suffered broken ribs and a punctured lung, filed a claim against the university, it launched an independent investigation that found differently.

San Jose State fired Silva and settled the case for $950,000. But Silva appealed to the state personnel board, which ordered him reinstated. He nevertheless resigned and was subsequently hired by Los Gatos-Monte Sereno, where Decena had taken a job as chief. No reason was given for why Silva quit his latest job on Friday.

In the East Bay case, records released under the new state law and contained in the divorce proceedings of Officer Josh Shavies show that he was fired for soliciting prostitution and dishonesty after filing a false police report related to his divorce.

He also was accused in the divorce proceedings of abusing his wife and whipping his children with belts. His ex-wife says now that she exaggerated the abuse allegations, but her attorney says they were completely truthful.

These cases raise questions not only about the temperament and effectiveness of the cops but also about the potential liability for taxpayers. These sorts of cases are yet another reason why the transparency law was so desperately needed — and why more departments need to start complying with it.