It happened at around 8.15pm when a silver car and a grey vehicle collided on the road between Skipton and Kildwick at the Cononley Lane end.
A North Yorkshire Police spokesman today said: "The silver car was travelling from the direction of Kildwick towards Skipton and collided with the grey vehicle which was travelling in the opposite direction.
"It is also believed that there may have also been a red vehicle was involved in the incident."
Officers are asking anyone who either witnessed the incident or the manner of driving of the vehicles prior to the collision to contact them with information.
Officers are also keen to speak with anyone who has dash cam footage which may help the investigation.
Contact North Yorkshire Police on 101, quoting reference 12180100373.