It occurred at around 8.45pm on Friday 26 September 2014, on Sowerby Road, involving a blue Audi TT and two pedestrians.
The Audi left the road and hit the pedestrians before colliding with a lamp post.
The men who are aged 39 and 20, both from York, were taken to York Hospital with serious but non life threatening injuries, where they remain in comfortable and stable conditions.
Following the collision the driver left the scene on foot.
Traffic Inspector Rich Champion, of the Force’s Roads Policing Group, said: If you are the man who was driving the Audi at the time of the collision, I am strongly urging you to come forward and contact the police immediately. It is in your own best interests to do so, before we locate you.
I am also asking anyone who witnessed the collision or can locate the driver to contact the police straight away.
Anyone who can assist with this enquiry should contact North Yorkshire Police on 101, select option 1 and pass the details to the Force Control Room.
Or call Crimestoppers anonymously on 0800 555111, quoting reference number 12140166099.