Mayor Rahm Emanuel would be nuts not to let a federal judge have oversight over the Chicago Police Department because there is no win for him if he doesn’t.

The reason is simple: lack of trust.

No matter what the mayor says, or how much money he spends lifting up depressed African-American communities, or how many aldermen reject a consent decree, trust has been broken.

The breakdown between police and citizens living in primarily black and brown neighborhoods didn’t occur because of the Laquan McDonald police shooting.

But the brutal execution of the teen — shot 16 times by a former Chicago police officer, Jason Van Dyke, who now awaits trial for murder — was the breaking point.

Now, it will take a federal judge and mandated oversight to restore even a fraction of trust.

       OPINION

The suspicion cuts both ways. The head of the Fraternal Order of Police, Kevin Graham, let it be known that he doesn’t trust the advocates behind the suit, referring to them as the “anti-police movement.”

But this isn’t a rag-tag group of protesters. They are energized, organized and unified.

When the mayor floated the idea of an “independent” monitor without court oversight, they were ready with a class-action lawsuit, filed this past week, against the city of Chicago and individual police officers. The lawsuit names six individuals and seven community groups as plaintiffs.

One of those plaintiffs, Women’s All Points Bulletin, has been asking the feds to investigate the Chicago Police Department for more than a decade. WAPB was one of the groups that pushed for former Detective Dante Servin to be criminally charged in the fatal shooting of 22-year-old Rekia Boyd in 2012 while Servin was off-duty.

Servin was charged with involuntary manslaughter and ended up being acquitted in a bench trial based on the judge’s reasoning that Servin was charged incorrectly, pointing to a lack of “reckless conduct.”

According to Illinois Attorney General Lisa Madigan, who met with the mayor, Emanuel is “scared” of federal court oversight over the Chicago Police Department and the decades of financial pressure that would impose.

But the city has paid about $662 million on police misconduct since 2004, according to Crain’s Chicago Business. And it is estimated that astronomical amount will keep climbing because there are hundreds of police misconduct cases in the pipeline.

So for elected officials to worry now about what federal monitoring of the Chicago Police Department would cost is lame.

Crista Noel, co-founder of WAPB, was in federal court on Friday monitoring a federal lawsuit against the Joliet Police Department when I caught up with her about the class-action suit.

“We have done years of work around trying to get the Department of Justice to investigate the Chicago police,” Noel said. “We have been asking for a consent decree since 2013. We kept asking: What does the Chicago Police Department have to do in order for y’all to investigate them?

“Rekia wasn’t enough to bring them out. It took that little pip, and Laquan was that pip,” she said.

Among other things, the lawsuit seeks the appointment of an independent monitoring team reflecting the diversity of Chicago’s communities “which will report to the federal court on the status of CPD’s compliance with the order.”

“We don’t want money,” Noel said. “We want to do transformative change. The Chicago Police Department trains most of the police in Cook County and Illinois. If you can get them to act right, you can affect almost every police officer that comes under their training.”

She views the the mayor’s “independent” monitoring idea as a non-starter because “we don’t trust him.”

“You need oversight, and you need oversight that come back and monitor,” Noel said. “When you have an opportunity to stop monitoring whenever you want, there is a problem.

“I understand the community is responsible for monitoring the Chicago Police Department, as well. And at some point in time, we were falling down on our job. But now we are here, and we are ready.”

The mayor should take the federal oversight and consider it a blessing.