Does anyone think that Starfleet does police work on planets?

I know they serve to defend the Federation but I was wondering if they worked with local authorities on police stuff regularly.

I DON'T THINK SO, UNLESS IT IS DIRECTLY AFFECTING STARFLEET IN GENERAL. SUCH AS TERRORIST ATTACKS, ,SOMETHING FROM SECTION 31 OR A DISASTER. ONE I THINK IT WOULD SPREAD IT TOO THIN AND STARFLEET IS BIG ON SELF GOVERNING WHICH WOULD GO WAY AGAINST THAT. BUT I COULD BE WRONG, JUST MY HEADCANNON.

I would say yes, but in extremely limited circumstances. First, the planetary government will have to ask. Second, the problem involves Starfleet in one form or another, like the initial problem can be traced to Starfleet, or whatever is going on will affect Starfleet, like in one novel when antimatter was used on Centauri. Other than that, Starfleet will keep its snouts out of it.

Edit: the novel is 'Crisis on Centaurus'. Good luck finding it.

We see Starfleet deployed on Earth under martial law during the DS9 two parter, but that's martial law. Under normal circumstances, as Starfleet is effectively the military, it wouldn't make sense for them to police outside of places where MPs would police IRL.

No, there is precedent for the federation’s equivalent of the FBI which is Federation Security, Dr. McCoy is arrested and taken into protective custody by them in the bar in Star Trek 3 before handed over to Star fleet security. We have also seen in multiple episode each planet has local law enforcement. Star Fleet Security is more analogous to the military police.
Star Fleet involvement in “Crisis on Centaurus” is initiated because of three civilian relief ships being destroyed by anti-ship missies from the planet. Also the involvement of weapons of mass destruction. Federation does not apparently have a version of posse comitatus act since they also act a the equivalent of the US Coast Guard.

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I appreciate everyone's insight.

I asked because I have been watching The Rookie, a cop show. And I think it's made me want to do a police style episode in my story Star Trek Equestria Reformatted.