Conduct your own forensic investigation
Has the transmission been recently replaced? Has the engine received recent repair work? What about the suspension? These are the three big expense components of most police vehicles, and to figure them out, you need to contact the official who posted the online listing. Or, if the government agency in question isn't online quite yet -- yes, that still happens -- contact the maintenance department and find out who keeps these records.
Either way, ask the official when you can come by and see the records in person, and whether there is a specific time of day when you can inspect the vehicle. Every place has rules and policies that are set in stone.
Start it up and look around
Some places will offer an escort and a battery jumper, while others have folks who will simply point, grunt, and let you do the heavy lifting of hoods, etc. Most car batteries will be DOA so make sure you have some juice with you if the agency won't give you a jump box.
In nearly all cases you will be allowed to start the vehicle up and do a detailed inspection, but driving the car is not an option. As for the records, it's almost always best to go over them with a fine-toothed comb beforehand because you really have no idea what you're getting yourself into otherwise.