The driver of a car failed to stop following the incident at around 7.35am on Sunday 8 June 2014, on the A61 at the roundabout in Ripley.
Both the cyclist and the small silver vehicle involved were travelling from Ripon to Harrogate.
As the vehicles crossed the roundabout, the car passed the bicycle before turning left onto the B6165, Knaresborough Road.
As a result, the 51-year-old woman cyclist fell from the bike, suffering serious injuries to her right hand shoulder and elbow, which required medical treatment as hospital in-patient.
Traffic Constable Stuart Holden, of the Force’s Roads Policing Group, said: It may be that the driver of the car involved in this collision is unaware that the incident took place. If this is the case I urge them to come forward and contact me so that I can take a statement from them.
I am also keen to speak to anyone who witnessed the collision or has any information which could help with this investigation and ask them to get in touch.
Anyone who can assist with this enquiry should contact Harrogate police on 101, select option 2 and ask for Stuart Holden. Alternatively, information can be emailed to firstname.lastname@example.org.
Please quote reference number 12140093960.