Occupants from the silver Fiat Doblo, taken from Stonepark overnight on March 7, fled the scene of the crash between Taunton and Bridgwater.
They also left behind a handbag which they had snatched during their raid on the Ashburton property.
Police are anxious to hear from anyone who may have seen or heard something suspicious in Stonepark on the night of March 7 and early hours of March 8.
They are particularly keen to hear from witnesses who saw the Fiat being driven away from the address.
Anyone with information should ring police on 101, quoting CR/015139/16.