Valerie Galloway, 53, is currently in a "stable" condition in hospital at Halifax Royal Infirmary.
She was found with serious head injuries after police were called to the semi-detached house in the Ovenden suburb of Halifax, West Yorkshire, on Tuesday afternoon.
It is believed the bodies of David Galloway, 55, and his son Michael were found by an older son.
It is understood that Mr Galloway was self-employed and had recently been ill. Michael was said to be autistic and a pupil at a local school for children with special needs.
'Such a nice family'
A neighbour in Sandown Avenue, a secluded cul-de-sac, said the family had lived there for about three years and kept themselves to themselves.
The woman, who asked not to be named, said she heard "a commotion" coming from the house and then saw someone running about outside.
"It's unbelievable something like this has happened," she said. "They were such a nice family."
The neighbour said Michael was very friendly, but the family was a very private one.
Post mortem examinations on the pair were carried out on Tuesday night and the results are expected to be made public later on Wednesday.
Scenes of crime officers spent many hours at the house looking for evidence and talking to neighbours.
It is understood that detectives are not looking for anyone in connection with the deaths.
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