Depending on what continuity or media you're in, The Gotham City Police Department are either Batman's greatest allies...or his worst enemies. And there have been times that's been flipped around.
True, Batman and Commissioner Gordon have a friendship/partnership that allows them to fight crime together while "skirting" the law and some points. But all think of it that way. They see Batman as a vigilante, and nothing more, so some go after him.
In a recent Batman storyline, Batman actually became the only target of the GCPD, forcing them to go after him and no other crime, period. it got sorted out, but the scars still remain. And should another one come along? Gotham's finest might be going after Gotham's greatest hero once again.