Police received a call at around 1.15am after a group of people were seen involved in an altercation on Albemarle Back Road.
On arrival a car was seen to leave the scene after colliding with a parked vehicle.
Officers followed the car out of Scarborough and stopped it in the village of Burniston.
The occupants, two men from Newcastle, were arrested.
The 20-year-old passenger was arrested on suspicion of assaulting three people and the 30-year-old driver was arrested on suspicion of dangerous driving and failing to stop following a collision.
They both remain in police custody for questioning.
Anyone with any information about the incident is asked to call North Yorkshire Police on 101, select option one and pass information to the Force Control Room, quoting incident number 12170071444
Information can be passed on anonymously to Crimestoppers on 0800 555 111.