Police say a 31-year-old woman, and 34-year-old man were found dead at a property in Hamilton, a small rural town 70km from Hobart, about 5am (AEDT) on Sunday.
The alleged offender, a 59-year-old man, was later found at Lachlan with a gunshot wound to the head and remains in Royal Hobart Hospital in a critical condition.
The ABC quoted police as saying that the nine-year-old girl told them her mother and her mother's partner had been shot.
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The girl also said a one-year-old boy, believed to be the alleged gunman's son, had been abducted from the property.
The ABC reports that the little boy was found in a car unharmed.
