The cyclist, a 35-year-old local woman, suffered three fractures to her neck when her bike collided with a blue Ford Fiesta on Westgate at around 1.30pm on Monday 14 April 2014.
She was taken to Friarage Hospital in Northallerton for treatment to her injuries.
Officers believe that a number of people will have seen the collision and are urging witnesses to come forward with information.
Anyone who can help officers with their enquiries is urged to contact North Yorkshire Police on 101 – select option 2 – and ask for Traffic Constable Don Wright or Thirsk Roads Policing Group.
Alternatively, information can be emailed to email@example.com
Please quote reference number 12140059120 when passing information about this incident.