A mother-of-three whose death was deemed a suicide was killed by her unfaithful husband who set up the scene and then lied, a coroner has ruled.

But the man has rejected the damning allegations.

The initial police investigation into the death of 43-year-old nurse Helen Bird in a shed at her home south of Hobart in 2010 was also "inadequate".

A coronial investigation was reopened after a renewed police interrogation of the case, sparked in 2017, identified Bird's husband Mark had "played a role" in her death.

An initial coronial report, completed in 2011, ruled Helen Bird had taken her own life.

But in findings published today, coroner Robert Webster determined Mark Bird killed her by asphyxiation while she was "incapacitated", potentially after being made to inhale fumes.

He then placed her phone, a photograph and a letter on a nearby work bench to make it look like suicide.

Mark Bird bought flowers, went to Big W and to visit a mutual friend in a "contrived" effort to have an alibi, Webster said.

He also made an undisclosed visit to the woman he was having an affair with.

"Mr Bird then gave a false version of events to police, and to friends and family, that he had come home and entered the house, but Mrs Bird was not present," Webster said.

"(He) then said he went into the backyard and phoned her mobile, and upon hearing her phone was ringing ... entered the garage (and found her)."

Mark Bird has not been criminally charged and in an affidavit to the inquest "absolutely rejected" the assertion he was involved in Helen Bird's death.

Tasmania Police says investigations into the case are ongoing.

"In particular, we note the coroner's findings regarding the initial police investigation, and we will be examining the ... findings in detail," a police spokeswoman said.

Webster rejected the initial police hypothesis Helen Bird took her own life for several reasons, including there was no evidence she was a suicide risk.

"The evidence establishes Mrs Bird's children were her life," Webster said.

"She would not have left them behind particularly with someone (Mr Bird) who was incapable of properly looking after himself, let alone his children."

The letter, written by Helen Bird to Mark Bird, was not a suicide note but an ultimatum about their marriage which was at times unhappy, Webster said.

Helen Bird was found wearing professional clothing, indicating she fully intended to attend a training course as planned that afternoon.

Mark Bird had a "spending addiction" and conceded while giving evidence at the inquest he was extravagant with money.

When Helen Bird died he received her death benefit and his share in her life insurance payment - a combined AU$390,000 (NZ$428,700).

"After Mrs Bird's death, Mr Bird's spending continued unabated," Webster said.

Mark Bird, who has served jail time for fraud offences, was an untruthful witness and person, Webster said.

He couldn't remember or recall answers on more than 50 occasions, some relating to "very crucial" matters.

The renewed police investigation identified people who had not been included in the initial coronial investigation, Mark Bird's affair and undertook more testing in relation to the scene.

Webster said police should not accept what they are told about certain suicides until investigations conclusively establish otherwise.