Officers were called to the address at 11am by the ambulance service, following reports that a woman was unconscious.
She was pronounced dead shortly afterwards.
On Friday, a 39-year-old local man was arrested on suspicion of murder – but he was released on bail on Saturday, while enquiries continue.
The man and the deceased were known to each other.
Meanwhile, police are still treating the death as unexplained.
A post-mortem examination carried out at Worthing Hospital on Saturday 24 August was inconclusive, and further forensic tests are to be carried out in order to help establish the cause of death.
A police spokesman said: “It is still very early in the investigation, which is being carried out by detectives from the Surrey and Sussex Major Crime Team.
“We are trying to establish what happened and are following up all possible lines of enquiry.”