(Important Note: Per FAA regulations, government owned aircraft DO NOT have to undergo the same inspections as privately owned aircraft. So, its possible they maintenance costs would be somewhat lower for a police department, but being the government who knows.
What FAR?
Gov-owned, non-FAA-registered are under agency maintenance programs, but those would be limited to DoD and DoT Coast Guard airframes. Others, like police airframes, are FAA-registered. I've never seen a government exception to FAA regulations (not to say it doesn't exist).
But, even with exceptions, getting off a scheduled MX program would be foolhardy (not surprising, though, with fools running it) as, if they ever hope to sell the airframe, it's going to have to come back into compliance at sale. If the airframe does not have the pedigree, it will be unusable (or, at least, very expensive) to meet conformity for any certificated operator.