Vandals targeted a police car in Alfreton, denting its bonnet and breaking a llight.
Officers are appealing for help tracing the person responsible.
The liveried Vauxhall Astra was in a car park in Park Street between 11pm and midnight on July 26, while officers were attending an incident.
When officers returned to it, they found dents on the bonnet, rear passenger door and front passenger door, footprints on the windscreen and roof and a broken light.
Anyone with information should call police on 101 or Crimestoppers on 0800 555 111.