The bodies of Jeff Cheetham, 37, his wife, Beverley, 36, and their sons Christopher, 10, and Karl, 8, were found at their home in Brimington, near Chesterfield, shortly before 10am yesterday.
The body of Gladys Stevens, 79, was found in her home next-door to the Cheethams', but her death is not thought to be connected to the suspected leak.
Detective Superintendent John Langley said: "There's nothing suspicious to suggest the family had been assaulted or attacked or that they had taken their own lives. We are investigating the possibility of carbon monoxide poisoning being the cause of death. Three of our officers who attended smelt something unusual and complained of headaches. They were taken to Chesterfield Royal Hospital but released after treatment and are fine."
Consumer Affairs Minister Kim Howells said he was shocked by the news. He said: "It is a very sad and poignant reminder to us all that carbon monoxide can strike without warning, even where we feel safest, in our own homes."