The collision happened on the A61 Harrogate Road in Dunkeswick, close to the Weeton Lane junction, at 7.30am on Sunday morning.
A small red car, a small silver hatchback car (possibly a Vauxhall Corsa) and a grey Ford Focus were travelling south towards Harewood and a maroon Vauxhall Vectra was travelling in the opposite direction.
It is believed that the silver hatchback car overtook the small red car, the maroon Vauxhall Vectra then immediately collided with the grey Ford Focus.
The silver hatchback car and the red car both failed to stop.
Whilst the Vectra and the Focus (pictured) were both severely damaged, both drivers escaped with only minor injuries. Both men attended hospital where they were discharged later that day.
Officers investigating the collision are appealing for information and witnesses.
In particular they would like to speak to the drivers of the small silver hatchback and the small red car that were in the area at the time of the collision.
Anyone who witnessed the collision or has any information including dash-cam footage that could help with enquiries is asked to call North Yorkshire Police on 101, select option 2, and ask for Rob Roberts or email [email protected]
Please quote reference number 12180041868 when passing on information.