50-year-old Jacqueline Cowdrey, known as Jacqui, was found dead in her ground flat in Heron Court, Victoria Road, Worthing, shortly before 6pm on Tuesday (19 November)
A post mortem was carried out on Wednesday but further tests need to be done to confirm the cause of death.
Detective Inspector Gordon Denslow said: “We are still trying to confirm exactly what happened to the woman in the hours before her death.
“We believe she was in an argument with a man in Bedford Row, close to the Vintner’s Parrot pub in Warwick Street. Did you see or hear that argument taking place, some time between 4pm and 7pm on Monday (18 November) ?
“We would still also like to speak to anyone who may have seen or heard anything suspicious at Heron Court in the hours before we were contacted.
“Please contact us if you know anything at all about what happened.”
Anyone with information should call 101 or email firstname.lastname@example.org quoting Operation Seal, or call the independent charity Crimestoppers anonymously on 0800 555 111.”