The wing mirror of a green Vauxhall Astra was damaged and dents were made on the front offside wing when it was left parked and secure on St Nicholas Road in Beverley.
The criminal damage happened some time between 1600hrs on Friday 17 February and 0820hrs the following day.
Police want to hear from anyone who saw or heard anything suspicious or who knows the identity of the person responsible.
Anyone with information is asked to contact Humberside Police on telephone 101, referring to log 443 of 20 February 2012.