UPDATE: THE man suspected of killing a Tasmanian couple at the weekend is in a coma under police guard in at Royal Hobart Hospital.

A man, 34, and a woman, 31, were found shot dead at a home at Hamilton, northwest of Hobart, yesterday morning, after the woman's nine-year-old daughter called police.

The suspected gunman, 59, who was previously in a relationship with the woman, was found in his car with a gunshot wound to his head at Lachlan, 45km from Hamilton.

A police spokesman said the man was yet to be charged.

A one-year-old child and a nine-year-old girl were found in the car with the man. Neither of them were injured.

The man's car has been seized and forensic examinations are under way at the Hamilton property.

The killing had caused "significant concern" in the small town, police said.

A public plea has been issued by police for background information about the couple, and the relationship between the suspect and the two victims.

They said earlier there were no reports of violence between the woman and her suspected killer.

The two children and the woman's elder daughter are now being cared for by relatives.