North Yorkshire Police's Roads Policing Group was on a proactive patrol last week when they were alerted to a dark-coloured Suzuki Swift which failed to stop at an officer's request to pull over.
Officers said a short pursuit ensued with the driver taking a turn onto a grass track, eventually abandoning the car, and making off on foot with the car's passenger.
However, the driver could not outrun the National Police Air Service and was quickly located.
He was arrested on suspicion of driving dangerously and failing to stop for police. The car was also found to have no insurance and so was seized.
Officers had initially attempted to pull the driver over for not having an MOT, and therefore the car was not roadworthy.
The driver was interviewed and later released under investigation while enquiries continue.
The arrest occurred during North Yorkshire Police's "Proactive Fortnight" – a two-week crackdown on county lines drug dealers, those involved in cross-border and rural crime, dangerous drivers and increasing the safety of women and girls on nights out.