The vehicle has been left damaged after the incident in Thoresby Road, Acomb, at about 2am on Sunday (June 8).
North Yorkshire Police said no one was inside the car and no one was injured during the incident.
The force said a window of the car, a Renault Modus, had been smashed and the interior set on fire.
“The fire service attended and put out the fire. The vehicle was parked on the street unattended, with no one inside, and no one was injured during the incident,” a police spokesperson said.
North Yorkshire Police urges anyone with information about the incident to contact the force.
“We're asking local residents to check any CCTV or video doorbell systems, or get in touch if they saw or heard anything that could assist enquiries,” the police spokesperson said.
Those with information are asked to email ethan.sampson2@northyorkshire.police.uk or phone 101 and ask for PC 1450 Ethan Sampson.
Crimestoppers can be contacted anonymously on 0800 555 111 or via their website.
Quote police reference number NYP-08062025-0047 when passing on information.
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