The force want to speak to the woman, who is believed to be in her 50s, after a female shopper allegedly had her purse stolen while Christmas shopping at the Entertainer toy store at about 10.10 am on Saturday 24 November.
The suspect is white, with short, cropped brown hair. At the time of the alleged offence, she was wearing a black jacket, black trousers, black shoes and white gloves. She was carrying a black handbag along with a white plastic bag.
Anyone with information is being asked to phone the States police on 612612 or Crimestoppers on 0800 555 111.