to cop or not to cop

So a wrangle with out of state plates was in my state today. Some car was tailgating this vehicle. He flipped on his undercover red and blue lights. Tailgating vehicle backed off.

Question is this - is an out of state police with police lights mounted in their personal vehicle* able to flip lights on and/or pull someone over while out of state? Is it... police impersonation? 

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Wrangler had vanity plates so I assume it was a personal vehicle. I don’t know the rules for mounting official police lighting in their car.