The collision involved a motorbike and another vehicle, believed to be a car, and happened at the roundabout between Somerset Terrace and Vernon Road at 11.45am on Sunday.
The motorcyclist came off his bike, sustaining a minor injury to his leg, and the other vehicle left the scene.
Officers are keen to hear from anyone who saw what happened and might have information about the other vehicle involved.
Anyone who can help should call North Yorkshire Police on 101, select option two, and ask for PC 336 Hinchcliffe.
You can also email [email protected], quoting police reference number 12200165416.
Information can also be passed on anonymously via Crimestoppers on 0800 555111.
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