North Yorkshire Police were called at around 6pm on Saturday April 16 after a silver VW Golf was driven "erratically" around Foreshore Road and Marine Drive in Scarborough.
Officers said the two men were seen hanging out of the windows and also allegedly got out of the car on several occasions to threaten passers-by with violence.
Police attempted to stop the car on the A171, near The Flask Inn, but the driver sped off and collided with another car.
Later that night, the car was spotted by officers in Pickering. The driver sped off again, heading towards York, but was brought to a stop by a stinger – a sliding strip of spiked metal designed to deflate tyres.
Two men, aged 37 and 23, who were both passengers in the car, were arrested on suspicion of a number of offences. Both men have been released under investigation, police said.
Officers are urging anyone with dashcam footage of the car or anyone who was involved in an altercation with the car's passengers to come forward by calling 101, pressing 2 and asking to speak to TC Mark Patterson or email [email protected]
Quote police reference number 12220064380 when providing information.