The rider, a 46-year-old local man, suffered serious injuries to his ankle and arm when he was forced off the Knaresborough to Wetherby road at around 8.25am on Tuesday 20 September 2011.
He had just passed the roundabout at the junction with the A658 when he was overtaken on a bend by a small silver vehicle carrying three young men. As the car overtook the moped it cut back across its path to avoid a vehicle travelling in the opposite direction.
The moped rider had to veer to the left to avoid a collision and fell from his bike after hitting the grass verge at the side of the carriageway.
He was taken to Harrogate District Hospital where he remains in a stable condition.
Officers are appealing to anyone who witnessed the collision to come forward with information.
Traffic Constable Stuart Holden, of Harrogate Roads Policing Group, said:
The rider of the moped had to take evasive action to avoid a collision and sustained some injuries which may require surgery as a result.
I am appealing to anyone who witnessed the incident to contact the police as soon as they can.
I would urge the occupants of the silver-coloured vehicle that overtook the moped prior to the rider falling off, to come forward as they may have information vital to the investigation.
Anyone who can help the police with their enquiries is urged to contact TC Stuart Holden, of Harrogate Roads Policing Group, on 0845 60 60 24 7, quoting reference number 12110159729.