The emergency services were called to the property at Redburn, Bonhill, at about 03:00 on Tuesday.
Police said they were trying to establish if there was "any criminality involved" in the blaze.
There have been a number of wilful fire-raising incidents in the area recently, but police do not believe they are linked to the latest blaze.
Det Insp Andy Doherty, from Clydebank CID, urged anyone who was in the area between 21:30 and 00:30, and who noticed anything suspicious, to get in touch.
He said: "Extensive inquiries are under way to establish how the fire started and if there is any criminality involved.
"We are aware of a number of recent wilful fire-raisings in the area. However, at this time we do not believe this morning's fire is linked to these other incidents."
A 44-year-old woman is in a critical condition in hospital after a fire at a house in West Dunbartonshire.