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.
Alternatively, information can be emailed to email@example.com
Please quote reference number 12140059120 when passing information about this incident.