Police are trying to piece together Susan Monkhouse's final movements after she was found dead in her home, in South Street, Greenock.
The discovery was made at around 5.40pm on Wednesday but it is not yet clear how the 49-year-old died.
Police confirmed a post mortem has taken place, but further inquiries are being carried out to establish the exact cause of death. Detectives are treating her death as "unexplained".
Officers have been speaking to neighbours and studying CCTV in a bid to find out more about how she died.
They have established Ms Monkhouse was alive on Monday night.
Detective Inspector David Wagstaff, who is leading the investig-ation, said today: "Susan Monkhouse was last seen at 9.30pm on Monday, when she was dropped off at her home after a night out in Greenock. I would urge anyone who saw Susan between Monday night, when she returned home, and late Wednes-day afternoon, to come forward as a matter of urgency.
"I would also ask anyone who lives in South Street, or who regularly visits there to think back and come forward to police if they witnessed anything out of the ordinary, or anyone acting suspiciously."
Anyone with any information is asked to contact police on 01475 492500.