At around 8.10pm on Saturday 29 September 2012 the cyclist, a 19-year-old woman, was riding along the A6108 between Cover Bridge and Middleham when she was hit from behind by a passing vehicle.
The impact forced her off her bike onto the grass verge at the side of the road and she suffered minor cuts to her head.
The vehicle did not stop at the scene of the collision.
Officers are appealing to anyone who witnessed the collision or was in the area at the time of the incident, to get in touch.
Anyone who can help officers with their enquiries is urged to contact North Yorkshire Police on 101 – select option 2 – and ask for PC Andy Foster or Leyburn Safer Neighbourhood Team.