I’m surprised nobody has mentioned what I believe to be the more common answer:
Once a police department is finished with a car that has become too old, the department often removes its markings and auctions it off.
If you don’t see any government markings anywhere (such as the license plate), I’d guess it’s no longer a police car (based on my experience in the southwestern USA), and the chances of the driver instructing you to do anything (i.e. impersonating a police officer) are very low.
But if someone in such a car did announce that they were a police officer, and they did not have an official uniform on with a badge, I'd call 911 and report them (since officers in an unmarked police car must be in full uniform, at least in certain states—I recommend researching the particular state you're in).
Retired 2006 Dodge Charger Police Car:
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GovDeals and Public Surplus are the kings of online auctions
and regularly liquidate cop cars for local municipalities. There are
thousands of cars to choose from, ranging from mint-condition cherry
rides that have barely been put through their paces, to those
unfortunate many that have been smashed to hell and have potentially
fatal amounts of bodily fluids staining the seats.
Currently, in the United States and Canada, the paint scheme for each
fleet is determined either by the individual agency or by uniform
state legislation as in Minnesota. Usually, state laws exist that
establish standards for police vehicle markings, and proscribe
civilian vehicles from using certain markings or paint schemes as is
the case in California.
Today, most fleet markings on patrol vehicles are created from
reflective vinyl with an adhesive backing that is applied in a
peel-and-stick manner. Colors chosen to represent the departments
identity are typically chosen by the individual department, although,
as noted above, some states have specific guidelines for color schemes