It occurred shortly before 8am on Wednesday 17 July 2013, at the junction of Kings Road and Alexander Road.
The collision involved a pedal cycle heading into the town and a maroon five-door saloon car which pulled out of Alexander Road. The 30-year-old local man riding the bicycle braked to avoid hitting the car and came off the bike, suffering a possible broken elbow.
The woman driving the car stopped to ask how the man was before leaving without passing on her details.
She is described as Asian, aged in her late thirties or early forties with a slim build.
Travelling behind the saloon car was a dark coloured 4×4 type vehicle.
Charles Ferguson, of Harrogate Safer Neighbourhood Team, said:
If you were the woman driving the maroon saloon car I urge you to come forward straight away as I need to speak to you as part of my investigation.
I am also keen to speak to the occupants of the 4×4 as I believe they will have had a clear view of the incident and as that they get in touch straight away.
Anyone who witnessed the incident or can help to identify the woman driving the car is asked to contact Harrogate police on 101, select option 2 and asked for Charles Ferguson. Alternatively information can be emailed to firstname.lastname@example.org, quoting reference number 12130120261.