In particular they want to trace the occupants of a black Land Rover Discovery and a white Ford Focus who were travelling into the village of Sherburn.
At around 7.45pm on Sunday evening, a number of people were assaulted during a disturbance at the Crow’s Nest caravan park near Gristhope, Filey.
The suspects, a man and a woman who were later arrested, then left the scene in a grey Vauxhall Astra in the direction of Scarborough.
A short time later officers sighted the vehicle at Staxton on the A64 where it failed to stop for them.
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Attempts were made to stop the Astra near Potter Brompton using a stinger device but it continued along the A64 driving at speed.
At one point, near West Heslerton, the vehicle stopped and reversed into a police car before continuing towards Scampston where it eventually stopped.
A 29-year-old man then ran off from the vehicle into nearby fields where he was arrested following a short foot chase. The woman, 31, who remained in the vehicle was also arrested.
A number of motorists had to take evasive action to avoid the Astra as it drove along the A64.
Police are appealing to those motorists and to anyone who witnessed the car travelling along the A64 to contact them, particularly the occupants of the Land Rover and Ford Focus and anyone who has dash-cam footage of the vehicle.
Anyone with any information is asked to contact North Yorkshire Police on 101, select option 2 and ask for Scarborough CID. Or email CIDScarborough&[email protected]
Please quote incident number 12190094916 when passing on information.
During the incident at the caravan park, two men sustained cuts, one to his head, the other to his leg.
The two people who were arrested remain in police custody at this time.