Lorraine Head, 46, also known by the nickname George, had suffered a head injury. Her body was found on Friday night at the cottage where she lived in Kings Head Mews, Rogate, West Sussex. There were no signs of a break-in and nothing had been stolen, said Sussex Police.
A 57-year-old man arrested on suspicion of murder was released on bail until 7 July. No charges have been brought against him.
Detective Chief Inspector Steve Johns, of Sussex Police's major crime branch, said: "Lorraine's head injury is consistent with her having fallen down the stairs, and at this stage one of our principle lines of inquiry focuses on the possible reasons for that."