Kelly Webster, 36, and her daughter, Lauren Thornton, both from Leyland in Lancashire, died while on a boating holiday in Windermere in the Lake District on Monday.
Cumbria Police said Ms Webster's partner, Matthew Eteson, 39, also from Leyland, was the third person on board the private vessel.
Mr Eteson, the owner of the boat, has been released from Royal Lancaster Infirmary following treatment.
Police said Mr Eteson raised the alarm after experiencing breathing difficulties.
Detective Inspector Mike Brown, who is leading the investigation, said Ms Webster and her daughter were both found in the rear of the boat.
He said he believed the deaths of Ms Webster and her daughter "may be as a result of carbon monoxide inhalation".
He said: "What we are looking at specifically is an aftermarket generator that has been fitted in the engine compartment of the boat, which we believe may be the cause of this.
"But, again, it's still early stages in the investigation so we can't rule anything out."
Mr Brown added: "It's an absolute tragedy. Everyone is in bits over this."
Mr Eteson, who lived with Ms Webster in Leyland but is not Lauren's father, is listed as a director of family firm Etesons Ltd, which specialises in plumbing, heat and air conditioning installation.
Cumbria Police were called to a jetty near Bowness at around 4pm by the ambulance service after it was reported that three people on a privately-owned boat were having serious breathing difficulties.