A woman's decomposing body lay in the hallway of a home she shared with a man for weeks before being discovered by a relative after the man was detained for a medical assessment.

The 61-year-old woman's body was found on Saturday by a family member of a 55-year-old man who lived with her at a New Town home in Hobart's north.

Police and members of the acute mental health team had attended the property on Saturday morning to take him for a mental health assessment but did not enter the cluttered home, Tasmania Police Detective Inspector David Gill said.

'The mental health team and police have spoken to the male person at the residence where he was immediately detained for that mental health assessment and conveyed to the Royal Hobart Hospital,' he told reporters.

'It wasn't until later that day that another person attended the address to visit, and then found the body of the deceased woman on the floor.'

Det Insp Gill said it was apparent the woman had been dead inside the house for a number of weeks.

'The male person has not made any disclosures of any form to members of Tasmania Police,' he said.

Det Insp Gill confirmed the man's mental health referral was made by someone else, and said he was being held at the Hobart Reception Prison after completion of his treatment while investigations continued. 

'At this stage, he has not been charged with any offence,' he said.

The home the pair had shared for some time was 'chaotic', with clutter everywhere.

'When police attend any scene where a person is deceased, it's obviously confronting and distressing, and this was no different,' Det Insp Gill said.

Police are treating the woman's death as suspicious, given she had been dead inside the house for weeks, but are keeping an open mind to her dying from natural causes.

An autopsy will be performed on Monday to ascertain the woman's cause of death.

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