Police say they are keeping an open mind about whether there were any suspicious circumstances surrounding her death after the body of the woman, believed to be her in 30s, was found at an address in Bence Court in the town on Friday afternoon.
Formal identification has not yet taken place, but the woman’s family are being supported by specially-trained officers.
Anyone with information which could assist the investigation is asked to contact the Brunel Major Crime Investigation Team on 101, quoting Operation Majesty.
A man arrested in connection with the death was released under investigation.
The 35-year-old man from Amesbury was arrested yesterday on suspicion of murder and released today, while enquiries continue.
Enquiries are ongoing and her death is currently being treated as unexplained.