Officers attended a collision on the evening of Tuesday, March 20, on the B6161 Leathley Lane.
A passing member of the public stopped and provided the coat to a shaken-up motorist.
However, he left before officers were able to give it back to him, and it is currently in storage at Harrogate Police Station.
North Yorkshire Police have shared a photo of the jacket on Facebook and Twitter in the hope that he will see it.
Anyone who knows who it belongs to is asked to call North Yorkshire Police on 101 and select option four.
People can follow the ‘North Yorkshire Police - Found Property’ page on Facebook and @NYP_Property on Twitter for updates on items handed in to police stations in North Yorkshire.
Items circulated in the last month include an Apple Watch found in Harrogate, an engraved pendant locket found in York and even an ice hockey helmet found in Skipton.