The incident happened at around 1am in the early hours of Sunday 28 September 2014 on Victoria Road at the corner of Esplanade in Harrogate.
The offending vehicle hit a 38-year-old woman, knocking her to the ground and then left the scene without stopping.
The woman was taken to Harrogate District Hospital where she was treated for minor injuries.
The driver of the vehicle is believed to be a man in his late 20s and there were also women or girls in the car.
Officers are appealing for the driver and passengers in the vehicle to come forward. Witnesses to the collision are also urged to contact the police and anyone who can help identify the driver of the car.
If you are the driver or a passenger in the vehicle, or have any information which could assist the investigation, please call North Yorkshire Police on 101, select option 2 and ask for Traffic Constable Steve Wood or email firstname.lastname@example.org
If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Please quote reference 12140166852 when passing on information.