Officers said the red Skoda Fabia, with the registration number FD10 LCL, was stolen from outside a property on Stonefield Avenue in Glasgow at some point between 1pm and 7pm on Sunday, December 13.
Police finally recovered the car when it was involved in a crash on the on-ramp for the M8 near Glasgow Airport, at around 7.15am on Monday, December 14.
It is understood to have veered off the carriageway and collided with a barrier.
Detectives said two occupants then scrambled from the scene of the crash on foot, and have yet to be seen since.
The crash caused rush hour chaos on the M8 as one lane remained shut for hours while emergency services dealt with the aftermath.
A search of the area was carried out by police with no trace of either person being detected. Nobody has since presented as injured as a result of the crash at local hospitals.
Detective Constable Diane Robertson of Greater Glasgow CID said: "Enquiries are ongoing and we would urge anyone who may have seen this vehicle or who witnessed the crash to come forward.
"In particular we would be keen to speak to anyone who may have seen the occupants of the car or to anyone passing who may have dashcam footage.
"Any information can be passed to Police Scotland, quoting incident 0427 of 14 December, or call Crimestoppers anonymously on 0800 555 111."