The incident involved a red Vauxhall Corsa driving in the Rawcliffe Lane area at around 7.45pm on Thursday 29 September 2011.
When the car reached Rawcliffe Drive it lost the front offside tyre however the driver did not stop. The Corsa was abandoned a short time later by the driver and a man who was a passenger in the vehicle.
A 23-year-old man was arrested in connection with the incident. He has now been released on bail to allow for further police enquiries.
PC Mark Proctor, of the Clifton Safer Neighbourhood Team, said:
It appears that the Corsa was being driven in a wholly unacceptable manner and was posing a danger to other road users.
I would like to speak to anyone who may have seen the Corsa travelling in the area prior to it being abandoned and asked that they contact the police as soon as possible.
If you can assist with this investigation please contact Mark Proctor, of York police, on 0845 60 60 24 7 quoting reference number 12110165413. Or call Crimestoppers anonymously on 0800 555 111.