A concrete slab was thrown through the window of a marked police car on Sunday afternoon.
An officer was attending an unrelated incident at around 2.05pm when a man caused damage to the vehicle as it was parked in Horners Croft, Greenleys, Wolverton.
He then ran away along the redway towards Gloucester Road.
The offender is white, aged in his late teens or early twenties, is around 5ft 5ins and was wearing a dark hoodie.
Insp Sally Kestin said: “This is an incident of criminal damage and such incidents will not be tolerated in Milton Keynes.
“If you saw the offender carrying out this act, or if you may know him from the description provided, then please call us on the non-emergency Thames Valley Police Enquiry Centre number 101.
“Any piece of information you have, no matter how seemingly insignificant, could prove to be a vital clue for us in our investigation.”
Alternatively, contact Crimestoppers anonymously on 0800 555 111.
No personal details are taken, information is not traced or recorded and you will not go to court.