Just owning and driving the car presents an interesting case.
Foe example, you could buy and drive a dark gray Crown Victoria and have a searchlight mounted on the driver door.
It wouldn't have any police markings, but 100% of the people you pulled up behind would think you were an unmarked police cruiser.
You could even wear a hat that would look something like a state police hat, something purchased in an ordinary store.
I posit that you would not be actually breaking the law, but you would be affecting other drivers’ behavior.