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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Thrillist says:
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 and markings.