Police investigating relationships in Devonport murder-suicide

At a press conference on Sunday, Detective Inspector Kim Steven confirmed jealousy was a motive police were investigating.

"Certainly, all three are known to each other and it's the relationship connections that we are looking at and what motive or motives are within that," he said.

"Whether that be jealousy or along those lines, that's probably the area we are looking at, at this stage."

The woman who was injured in the shooting remains in the Launceston General Hospital in a stable condition.

Two children, a 10-year-old and a 12-month old, who were present in the home during the shooting have been placed in the care of their grandmother.

Detective Inspector Steven urged Coastal residents to surrender unused firearms to Tasmania Police.

Earlier on Sunday, it was confirmed the Winchester shotgun the unlicensed Mr Carey had used was unregistered, and that he acquired it in the past three months.

"I want to make a plea for anyone who might have one of these unregistered guns that have been part of families or they have come across in the last decades, sitting in the back of the shed, in their roof, wherever it is, to have a think and please hand them in under the amnesty," he said.

"It may prevent one of these things from happening in the future."

When asked whether police were considering the attack to be premeditated, Detective Inspector Steven said the investigation was still underway.

He said Mr Carey had acquired the shotgun in the past three months.

"We want that person (who sold Mr Carey the gun) to come forward without fear of prosecution," he said.

"Unless that person comes forward and says 'I knew he was going to do what he was going to do'.

"Then that may change things a little bit."

Detective Inspector Steven was also asked whether Mr Carey was known to Tasmania Police prior to the shooting but he declined to directly answer.