Police are appealing for information after the crash happened at about 5pm on Saturday July 18.
The silver Audi A3 is believed to have been travelling towards Odsal, when it left the road and crashed into a garden wall, close to the junction with Rooley Crescent.
The road was closed for a short time while the vehicle was recovered.
Sergeant Penny Robinson, of the Safer Roads and Neighbourhood Support team, said:
“The vehicle suffered significant damage in the collision and it is important we trace the occupants, as they may have suffered injuries which need hospital treatment.
“We believe there were possibly two people in the vehicle, but enquiries locally and at hospitals in the area have failed to locate them.
“It is also possible that another vehicle was involved.”
Anyone who witnessed the collision, or who saw the movements of the Audi immediately before it, is asked to contact Bradford District CID on 101, quoting log *1154 of 18 July.