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][1], at least in certain states—I recommend researching the particular state you're in).

Retired 2006 Dodge Charger Police Car:
[![Retired 2006 Dodge Charger Police Car][2]][2]

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[Thrillist][3] says: 

> [GovDeals][4] and [Public Surplus][5] 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.

https://en.wikipedia.org/wiki/Police_vehicles_in_the_United_States_and_Canada#Skins/Paintjobs_and_Appearance:

> 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.


  [1]: https://www.youtube.com/watch?v=n1qnvv1nBoo
  [2]: https://i.sstatic.net/8Iryn.jpg
  [3]: https://www.thrillist.com/cars/nation/how-to-buy-used-police-cars-tips-tricks-for-cop-auctions
  [4]: https://www.govdeals.com/
  [5]: http://www.publicsurplus.com/