The body of the 46-year-old was discovered in the property in Newmilns, East Ayrshire, late on Friday evening.
A post-mortem is to be carried out to determine exactly how the woman died, but police are treating it as suspicious.
Officers remained at the scene yesterday and were said to be following a definite line of inquiry.
A force spokeswoman said yesterday: "[At] around 11.10pm last night the body of a 46-year-old woman was found within a flat in Loudoun Road, Newmilns.
"A post-mortem is due to take place to establish the exact cause of death. However, at this time we are treating it as suspicious and inquiries are continuing."