Kevin Baker, 35, died from "self-strangulation by ligature" while his wife Tracey, 42, had multiple head injuries, police said.
The couple, who are believed to have three children, were found at the house in Wellings Close, Chard, on Sunday.
Police began a murder inquiry but have said they are not looking for anyone else in connection with the deaths.
Avon and Somerset Police added investigations would continue "to develop a full understanding of what happened" and a file would be sent to the coroner's office.
Senior investigation officer Andy Mott said: "Our thoughts are very much with the families affected by this tragic incident and they're continuing to be supported by specially trained family liaison officers."
A man whose body was found beside his wife's at their Somerset home killed himself, a post-mortem has suggested.