A man stole a red Toyota Yaris at 5.28 pm last Sunday from Spring Hall Lane, Halifax.
He had turned up for a test drive.
The suspect is described as white, aged in his 30s, 5ft 4ins tall and of slim build.
He had a bald head or closely cropped hair and was wearing a black jacket, a white t-shirt and light stone-washed jeans.
Anyone with any information is urged to contact PC Will Burgess in Calderdale CID on 101.