Most cities sell their used police cars at local auctions. Some may also list them online on sites like eBay, and some private dealers buy them and resell them.
Cities that sell their police cars through auctions make that information public. Often, auction times and restrictions can be found on the city's website. Be sure to read the information carefully because many cities only sell to dealers or salvage yards to limit their liability. Avoid buying online from cities unless you are experienced because their ads may leave out important information.
Private dealers may resell police vehicles they buy at auction. Finding a reputable dealer that specializes in police vehicles is one of the safer ways to buy used police cars, especially if buying them online, as some police cars have significant mechanical issues. Dealers also generally fix cosmetic damage resulting from the removal of police equipment, such as sirens and radios.
Since many used police cars are bought by taxi companies, taxi maintenance divisions often keep track of used city vehicle sales and may be willing to pass that information along. Try calling them and asking if they know where to look. Some may even be willing to keep your name and contact information in case they come across a good car that they do not need.