Three vehicles collided on Aberford Road in Stanley, Wakefield, just before 8pm.
West Yorkshire Police said: "It was reported that one of the drivers had made off on foot from the incident, which involved three vehicles and saw several people treated for injuries at the scene.
"The road was closed for a short time to allow for the vehicles to be recovered.
"The Roads Policing Unit is continuing enquiries and anyone with information that will assist this investigation can contact the team on 101, quoting log 1205 of 26 December."