West Midlands Police say the 63-reg vehicle may be linked to car crime in the Wolverhampton and Dudley areas.
Footage has surfaced on social media showing a grey Ford Fiesta used by people trying to gain access to a BMW.
The video, published on Facebook, showed the vehicle stop outside a house on Dovedale Road, Wolverhampton.
A person, dressed in black clothing with a hood, emerges from the vehicle and steps over a small wall.
The figure then ducks down and approaches the car and tries the door handle.
The person then runs back towards the Ford Fiesta.
Another social media report said the same vehicle had been seen on Northway, Sedgley, where a strimmer was taken.
A spokesman fro West Midlands Police said: "We are investigating after receiving a number of reports of suspicious activity involving a grey 63-reg Ford Fiesta which may be linked to car crime in the Dudley area.
"Anyone with any further information is asked to contact with us, quoting crime reference number 20WV/290737P/20, via live chat at www.west-midlands.police.uk, 8am to midnight, or by calling 101 any time.
"Alternatively to tell us what you know not who you are, call Crimestoppers anonymously on 0800 555 111."
The video can be seen at https://fb.watch/1-x56Qk9-a