A car door was forced open in Tuddenham St Mary last week.
Police have said the cowling cover of the car was removed and it was left with wires hanging out in what appears to have been an unsuccessful attempt to start the vehicle.
The damage was caused between 1pm on October 11 and 7.40am on October 12.
The blue Volvo estate had been parked securely in a driveway in High Street.
Anyone with information is asked to contact PC Sarah Chapman at Mildenhall Police Station on 101 or Crimestoppers anonymously on 0800 555 111.