Krista Kach, 47, died in hospital last week following an incident in which she barricaded herself inside her Newcastle unit.
NSW Police said they were called due to reports a woman was threatening people with an axe, alleging officers were also threatened.
Several hours later, officers gained access to the unit and deployed a Taser, as well as non-lethal "bean bag" rounds, while attempting to arrest her.
Police said Ms Kach sustained a shoulder injury during the arrest, but she was able to walk to a nearby ambulance.
She was taken to John Hunter Hospital, where her condition deteriorated and she later died.
The incident is now subject to a critical investigation led by the state's homicide squad.
Ms Kach's family disputed police claims she was dangerous, saying she was simply distressed after being told she would be evicted from her unit.
They said police were told she was not well and needed medical help.
"We were assured that the police would look after our mother and that she would be cared for by a hospital and qualified medical professionals," the family said in a statement.
"What happened on Thursday was a disturbing and heartbreaking response by the police to a vulnerable person that had been told that she would soon be homeless."
The family said police did not tell them they had used a Taser in the arrest and instead they learned of that development on the radio.
They requested privacy but said they would be pursuing justice on behalf of their mother.
Ms Kach's death is the second fatal incident involving NSW police using a Taser in recent months after 95-year-old Clare Nowland died at a Cooma nursing home in May.
Greens MP and justice spokeswoman Sue Higginson called for a parliamentary inquiry into NSW Police after she obtained four hours of video filmed by Ms Kach in the lead-up to the arrest.
The footage reportedly includes her referring to the so-called "sovereign citizen" movement and various conspiracy theories.
Ms Higginson said a family member asked police at the scene if they could speak to Ms Kach to help try to calm her, but they were essentially told that doesn't normally work.
"Police responses and protocols escalate situations because they are driven by capture, custody and punishment," she said.
"The police are not equipped to deal with such situations, that's why we keep seeing vulnerable people killed at the hands of police."
NSW Police Association president Kevin Morton said officers shouldn't be handling serious mental health incidents.
"The mental health crisis team should be the people that are interacting with this, but there's been no funding for NSW Health to achieve this goal and at the moment it just falls fairly and squarely on the lap of police," he told ABC Radio on Monday.
Mr Morton said "the mere sight of the uniform" can agitate people who are mentally unwell.
"My plea to the government is if we are going to treat these people in the community ... then you need to fund these organisations so that they can get the right treatment and we don't have to call police."
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