Suspected Tasmania gunman yet to be charged

A man suspected of gunning down a couple in southern Tasmania remains in hospital and is yet to be charged, police say.

A man, 34, and a woman, 31, were found shot dead at a home at Hamilton, northwest of Hobart, on Sunday morning, after the woman's 9-year-old daughter called police.

The suspected gunman, a 59-year-old man who was previously in a relationship with the woman, remains in a critical condition in Royal Hobart Hospital.

He was found with a gunshot wound in his head in his car at Lachlan, 45km from Hamilton.

A police spokesman told AAP the man was yet to be charged and investigations were continuing.

A 1-year-old child found in the car with the man was not injured, nor was the 9-year-old girl.

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

Police have said there were no reports of violence between the woman and her alleged killer.

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