The collision occurred at about 10am on Monday 12 June 2017, on the A61 Ripon Road, between Harrogate and Killinghall, close to its junction with Knox Mill Lane.
It involved a blue Fiat Punto motor car, which was being driven towards Harrogate by a woman in her 50s, and a male pedestrian in his 30s, who lives locally.
The pedestrian was in the process of crossing the road towards Knox Mill Lane, having just got off a northbound Number 36 bus, when the collision occurred.
The pedestrian was taken to Harrogate District Hospital where he was admitted with a head injury. His condition is described as comfortable.
Officers are investigating the collision and would like to hear from anyone who witnessed it. They are particularly keen to talk to a woman who was driving a red car towards Killinghall, and who stopped to help at the scene, but left before police arrived.
Anyone with information is asked to call North Yorkshire Police on 101, quoting reference 12170102207.