The incident happened between 2am and 2.30am on Monday December 27 on Muston Road (A1039), Filey near the level crossing of the railway line.
A police spokesman said: "It involved an altercation between two people in a Blue Ford Ka that was stopped in the middle of the road.
"It was further reported that the car was later driven at one of those involved.
"In particular, we are appealing for the driver and occupants of a car that passed the couple while the incident was ongoing to come forward."
Anyone with information that could assist the investigation should contact North Yorkshire Police on 101, select option 2, and ask for Andrew Metcalfe or email [email protected]If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Quote the North Yorkshire Police reference number 12190235923.