The crash happened on the A637 Bar Lane between Flockton and Midgely, Wakefield, at around 10.15pm on Tuesday, August 4.
A silver BMW 1 Series and a silver Toyota RAV4, which were travelling in opposite directions, crashed into each other.
A woman in the BMW suffered serious, but none life threatening injuries as a result and was taken to hospital for treatment.
Roads policing officers investigating the incident would like to speak to anyone in the area at the time who may have witnessed the collision or seen the cars just before the crash.
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They would also like to speak to anyone who may have dashcam footage.
Anyone who can assist the enquiry is asked to please contact PC 6 Bastow of the Eastern Roads Policing Unit based at Carr Gate, Wakefield on 101, referencing collision 13200391512.