The crash happened on the A650 Bradford Road, East Ardsley, at the junction of Woodlands on Saturday, March 9.
Ambulance services alerted the police to the crash at about 1.30pm.
Police were able to confirm that the crash involved a Mercedes and a Peugeot 306 but were unable confirm the third car.
They also confirmed that one of the vehicles has been removed.
The video shows that one badly damaged car remained on the road at about 3.15pm.
Police said that there have been no serious injuries.
Bradford Road was closed off in both directions with police diverting traffic away from the scene.
Police confirmed that the road was cleared to reopen at about 3.30pm.