Man critical after Tasmania double murder

A man remains in a critical condition with a gunshot wound to the head and a man and woman in their thirties are dead in a double murder that has shaken a small Tasmanian town.

The bodies of a woman, 31, and a man, 34, were found at a property on Hamilton Plains Road at Hamilton, a small rural town 70km from Hobart, about 5am (AEDT) on Sunday.

The suspected gunman, a 59-year-old shearer, was previously in a relationship with the dead woman.

He was found at Lachlan, 45km away, lying beside a car pulled over to the side of the road, with a gunshot wound to the head.

Locals at Hamilton, which has a population of 300, say those who know the couple have been shocked by their deaths.

"It's not a nice thing to happen in the town," one local told AAP.

The woman's partner had been a local football player.

Detective-Inspector Colin Riley said the older man's gunshot wound was inflicted shortly before or just as a police car arrived.

The man was under police guard at Royal Hobart Hospital and in a critical condition after surgery.

Det Insp Riley said the woman's nine-year-old daughter called police using a mobile phone.

"It appears to me that the nine-year-old heard what occurred in the house and we are still ascertaining ... what was seen by that child," he told reporters at Hamilton.

He said the dead couple had been in a relationship and living in the Hamilton house for about four months.

There had been no reports of violence involving the dead woman and her alleged killer.

The children, including another daughter, believed to be aged about 13, who was not in the house at the time of the incident, were being cared for by their grandparents.