Three dogs also died at the property in Bedford Road in St Ives. Firefighters were called at 08:45 GMT.
Police, Cornwall Fire and Rescue Service and the Health and Safety Executive are now carrying out an investigation at the property with the help of CORGI Technical Services Incident Investigators.
Inhaling carbon monoxide reduces the blood’s ability to carry oxygen and can be fatal.
The colourless, odourless gas is produced by the incomplete burning of carbon-based fuels including gas, oil, wood and coal.