A MAN and woman have been found dead in an apparent double murder northwest of Hobart.

A woman, 31, and man, 34, were found dead at a property on Hamilton Plains Road at Hamilton, a small rural town 70km from Hobart, about 5am (AEDT) today, police said.

The alleged offender, a 59-year-old man, was later found at Lachlan with a gunshot wound to the head.

He is in the Royal Hobart Hospital in a critical condition.

Police have set up a command post at the scene.