Hmm...well, there are a few ways that you can do that depending on the disposition of the police chief. You should find out what he's like first. If he is the type to be flattered, or subscribe to gossip or slander, there is always going the 'journalism' route. If he is honorable and values this city, you are a concerned citizen, in this circumstance you may be able to recruit him to our cause.

Of course you must always keep in mind that his animosity towards the mayor may be a front just to draw out people like you trying to get information, and thus keep tabs of somethings we'd rather not have kept tabs of.