Alison McLaughlin, 53, and her husband Neil McLaughlin, 57, were found dead in an address on Banff Road in Greenock on Friday, January 5.
Emergency crews were called to the home following a report of concern for their welfare.
Officers have revealed that they are treating Alison’s death as murder.
They do not believe Neil’s death to be suspicious.
Following the discovery of two bodies at a property in Banff Road in Greenock, extensive enquiries have been carried out and officers are not looking for anyone else in connection with the deaths.
Detective Inspector Gordon Smith said: “Our thoughts remain with the family and friends of both Alison and Neil. They have asked for privacy at what is a very difficult time for them.
“I would like to thank the local community for their patience and understanding while we carried out our investigation.
“A report will be sent to the procurator fiscal.”