There's really no such thing as a 'Police pursuit car" only in people's minds and on half baked television shows.
Police vehicles are NOT chipped or enhanced for greater/better performance.
Police vehicle are fitted as many safety features as the manufacturer can provide - particularly for Patrol vehicles. This may include FE2 (improved handling - rougher ride), larger brakes (better stopping if severe braking applications involved in any driving), flashing warning/safety lights, siren, etc. In South Australia many unmarked Police vehicles are also fitted with the above safety features as their use may require 'emergency driving'. Occupant safety is paramount and the Police Department MUST provide a safe working environment and that includes suitable equipment.
Generally (because of above) such fleet vehicles are serviced in accordance with manufacturer's recommendations. To do otherwise MAY place employees at greater risk (remember ALL employees have significant responsibilities in regard to Occupational Health and Safety).
Some Police vehicle may have additional battery and electrical wiring to allow installation of above lights and sirens etc.
Some used Police vehicles MAY represent good value particularly if the distance travelled is moderate (perhaps less than 50,000km), regularly driven by the same person, this could be a Supervisor, Manager, country or specialised unit vehicle. Others may have been flogged and not particularly well looked after. No different than any other second hand fleet vehicle.
Generally, in South Australia, because such Police vehicles are leased, NOT owned by the Police Department, they are cleaned up to a very high standard, scratched, dented, damaged panels and other components are replaced with new. There may be some screw holes evident inside the cabin and under bonnet etc.