The blue Ford Focus was set on fire and severely damaged at around 10.10pm on Saturday, May 23, in Tillyloss, Kirriemuir.
Several other cars parked nearby were also damaged in the incident.
CCTV footage shows a man running away from the scene and getting into the passenger side of a grey Mini, which then drove away along Elm Street and Brechin Road.
Police Scotland is now asking for anyone who lives in the Brechin Road area who may have private CCTV footage to come forward to assist with their enquiries.
They have also highlighted that there is a potential witness they are trying to find, a man who was seen walking a “yellow-labrador type dog” on the south side pavement on Brechin Road at its junction with Elm Street.
If you have any information you should call Police Scotland on 101 and quote incident number 3759 of May 23. If you would prefer to give information anonymously you can contact Crimestoppers on 0800 555 111.