Officers went to a home on Walker Street at Sorell about 3.30pm on Wednesday and found the woman's body.
Neighbours earlier called the police, concerned they had not seen the woman for days. Police are yet to confirm whether the woman lived alone.
The community was close-knit and the neighbours dealt with each other regularly, Detective Inspector Rebecca Davis said.
She confirmed that while officers were treating the woman's death as suspicious, there was no further risk to the community.
"We can't rule anything out at this time," Det Insp Davis told reporters on Thursday.
"There are still a number of people that we would like to speak to in order for us to gain the full picture around the circumstances."
The community was deeply saddened by the woman's death, Det Insp Davis said.
Police, including forensic examiners, were on Thursday continuing to investigate.
Officers were seeking information about a motorbike seen in the area between last Friday and Wednesday, and wanted to talk to its rider.
"We should have some form of result in the next week," Det Insp Davis said.
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