Pennsylvania is a bit different than Racer72's reply.
In Pa, any citizen can bring charges against another person. The catch is that the charges must be approved by the District Atrtorney's Office (to prevent frivilous cases).
The citizen just goes to the District Court having jurisdiction over the location of the offense. They fill out the paperwork and submit it.
Different counties have different rules, though. In my county, you are required to report it to the police agency having jurisdiction prior to filing. If the police choose not to file, then you can do so on your own behalf.
Realistically though, if the police choose not to pursue charges, its most likely a weak case.