The yellow Seat Leon was stolen at knifepoint from a male driver and his female companion in Bay Hall Common Road, in Birkby, Huddersfield, on June 29 at around 9.45pm.
The suspect, described as an Asian male in his late 20s and around 5ft 7ins tall of slim build, was then seen driving at speed by a police car in Manchester Road, Bradford, at around 10.10pm.
Police officers then pursued the stolen car but were reversed into by the driver of the Leon, making the chasing vehicle undrivable. The Leon was found abandoned near Gibbet Street in Halifax on June 30.
The suspect had short black hair and was wearing a blue and black hooded top at the time of the offences.
Police Constable Kristen Ford, of Kirklees CID, said: “Clearly this has been a frightening experience for both victims, who fortunately were uninjured.
“I would appeal to anyone who was in and around the area of Bay Hall Common Road on the evening of June 29 and may have seen anyone acting suspiciously matching the suspect’s description to come forward.
“I would also appeal to anyone who was using the road networks that evening who may have seen the distinctive yellow Seat Leon being driven either through Huddersfield, Bradford or Halifax to come forward with any information. ”
Call police on 101, quoting log 13160278021, or Crimestoppers anonymously on 0800 555111.