Damage totaling £1,000 was caused to a patio door when thieves smashed it to get into a house on Sherwood Road, Tetbury, between 4.30pm on Friday November 17 and 9.30pm on Saturday November 18.
Up to 10 Xbox games worth a total of £300 were taken from a TV unit in the living room.
Although there was evidence the thieves had also been in bedrooms in the upstairs of the property, nothing else was taken.
While investigating the incident police also found a silver Nissan GTR parked on the road had suffered several deep scratches.
The owner confirmed the damage would have been caused between 1pm on Saturday November 18 and midnight on Sunday November 19.
Due to the close location and times of the two crimes, police are treating the incidents as linked.