Police were called to reports of a disturbance at a block of flats in the John Street area of the Dunbartonshire town on July 23.
Mairi Doherty, 41, sustained sustained serious injuries and was taken to the Queen Elizabeth University Hospital in Glasgow – where she died on July 26.
Police Scotland said two people, a man aged 43 and a woman aged 40, have already appeared in court after being arrested and charged in connection with the disturbance.
Officers have now launched a murder investigation, and have urged anyone who may have seen anything to contact them on 101 quoting incident number 0304 of July 23.
Detective Chief Inspector Stuart Grainger, of the force’s major investigation team, said: “Our thoughts are very much with Mairi’s family.
“This is a very difficult time for them and I want to reassure them, and the wider community, that we are doing all we can to establish the full circumstances of what happened.”
Mr Grainger added: “There were a number of people in and around the block of flats at the time of this incident and I would urge anyone who has not spoken to officers to get in touch.
“If you saw anything then please contact us, as even a small piece of information could help with our enquiries. In addition, if you have private CCTV footage that could assist, please make us aware.”
Murder enquiry launched following death of woman in Dunoon