Several marked police cars and the front of a police station were sprayed with petrol on Christmas Day.
A person was seen by officers squirting fuel from a washing-up bottle at about 05:30 GMT at Rugeley police station.
Police said officers inside the station could smell the fuel, but the offender ran off towards Anson Road as they went outside but were unable to catch them.
Staffordshire Police said the incident "could have been a lot more serious" if officers hadn't disturbed the offender.
The offender is believed to be in their late teens or early twenties and is described as of slim build, between 5ft 6in and 5ft 8in.
Police are appealing for anyone with information to come forward.