It is believed that the vehicle has been involved in a collision with a red Land Rover Defender, where it failed to stop.
It occurred near to Swinsty reservoir, on Sourby Lane in Timble.
At about 1pm on Friday 1 August 2014, as the Range Rover was heading towards Otley in West Yorkshire and the Land Rover Defender was going in the opposite direction.
The driver of the short wheelbase Land Rover Defender 90, a 20-year-old man from Otley, had to take evasive action and the vehicle ended up in a ditch.
A 19-year-old woman in the front passenger seat, also from Otley, suffered a suspected shoulder injury and was taken by ambulance to Harrogate District Hospital for treatment.
The driver of the Range Rover, which may have a black roof, is urged to contact North Yorkshire Police to assist the collision investigation.
Witnesses or anyone who can help to identify the Ranger Rover driver or owner are also asked to assist the police.
Please call North Yorkshire Police on 101, select option 2, and ask for Road Policing Group Harrogate. Or email andrew.macLeod@northyorkshire.pnn.police.uk
Please quote reference NYP-01082014-0225 when providing information about this incident.