It happened at a home in the Avon Mills Flats at around 8.10pm on Tuesday October 9, when an offender smashed a ground-floor kitchen window.
Witnesses saw a suspicious red vehicle in the area around the time of the burglary, which may be linked.
A spokesman from Wiltshire Police said: "Were you in the area at the time? Do you have dash cam footage or private CCTV which may show something? Did you see a red vehicle in the area which looked out of place?
"Anyone with information is asked to contact DC Jo Chesshire from the Community Tasking Team on 101, quoting crime reference number 54180095688. Alternatively you can call Crimestoppers anonymously on 0800 555111."