The incident took place near Nab Bridge, Pannal, at around 6.30pm on Friday, February 15 and involved a silver Kia Cee’d which left the road and came to rest on the embankment prior to the Harrogate-Leeds railway line.
North Yorkshire Police said: "The driver was a man aged in his 70s from the Leeds area. His wife was in the front passenger seat.
Both received minor injuries and were taken by ambulance to Harrogate Hospital. They were discharged following treatment.
"We are appealing for witnesses to the collision or anyone who recalls seeing the vehicle prior to the collision, to get in touch as soon as possible to assist the investigation."
The stretch of road was closed with local diversions in place while officers investigated the scene and to allow the vehicle to be recovered.
Witnesses are asked to contact Steve James on [email protected] or by ringing 101 and selecting option 2.
The North Yorkshire Police reference number is NYP 15022019-0514.