Police said two people in a Mercedes were pulled over in Strathclyde Park, Hamilton, South Lanarkshire, shortly after midnight on Monday by a car they believed was a police vehicle - a dark SUV with blue and red lights.
A man dressed as a police officer ordered both of them out of the car before assaulting the man in the passenger side and stealing the car keys.
He was then driven off in the SUV by a driver who was not identified.
Police said the suspect is white, with blond hair and stubble and wore glasses. He did not present any identification or a police warrant card.
There are no details on the driver of the SUV.
Detective Constable Gary Lipscombe said: "I'm aware that the circumstances of the crime will be of a concern to the public, but rest assured we are working hard to identify the suspects.
"We are currently studying CCTV footage from the surrounding areas and are gathering more detail on the car used by the suspects.
"I would also like to remind the public that police officers carry warrant cards that can be produced on request."
He asked members of the public in the area around the time of the incident to get in touch, particularly motorists with dash cams. He said: "Anyone with information is asked to call CID officers at Wishaw Police Station via 101, quoting incident number 0002 of 13 January 2020. Alternatively, if you have any information please call Crimestoppers on 0800 555 111 where information can be given anonymously."