Police went to the Keane Street residence on October 29 after receiving a concern for welfare from a friend who reported Veronica Corstorphine hadn't been seen for a month.

Officers found Ms Corstorphine's body on a bed, launching a 10-day investigation into the circumstances surrounding her death.

Police have alleged Ms Corstorphine was murdered on October 3.

The 46-year-old woman charged with murder lived at the Keane Street house for about two months before flying to Bunbury on October 5.

The two women are believed to be related.

Western Australian police arrested the woman at a Bunbury hotel on Thursday night, with four Launceston detectives flying to Western Australia to apply for an extradition order, facilitate the return of the woman and conduct further investigations with family members interstate.

Tasmania Police Detective Inspector Kim Steven said no one else was believed to be involved and there was no risk to the community.

Keane Street is divided by the Midland Highway, with the house in question on the west side. A normally quiet and friendly street where most of the neighbours are on first-name basis, the elderly woman was described as quiet and reserved.

One neighbour said Ms Corstorphine would wave or say hello, but she mostly kept to herself.

Several of the neighbours were unaware a second woman had been living with Ms Corstorphine.

One neighbour placed a bunch of flowers at the alleged victim's front door.

They all described a heightened police presence in the area over the past week, with officers making inquiries with neighbours, staying overnight in the street and scouring through rubbish bins.

Detective Inspector Steven said eight detectives had worked on the case since the body was discovered, with forensic officers and scientists spending several days at the scene.

It was alleged a number of Ms Corstorphine's personal items were missing from the house.

Detective Inspector Steven said police know the cause of death, but weren't prepared to release that information just yet.