An inquest into the death of a young woman shot by police in Sydney's west three years ago has heard the police response may have been inadequate.

There were multiple calls to Triple Zero after Courtney Topic, 22, was spotted brandishing a large kitchen knife outside Hungry Jack's at Hoxton Park in 2015.

She was seen to use the tip of the blade to brush hair from her face and was talking to herself as she sipped from a takeaway cup.

Courtney Topic, 22, was probably suffering from an untreated psychosis, a psychiatrist found after her "violent" death. (AAP) (AAP)

An officer shot Ms Topic just 41 seconds after arriving at the scene. (AAP) (AAP)

Police arrived under lights and sirens, drew their weapons and shouted.

The court heard capsicum spray was used, but it was after a Taser malfunctioned that the senior constable fired the fatal shot, 41 seconds after arriving on the scene.

Today, Counsel Assisting the Coroner, Gerard Craddock SC, told the inquest neither officer could remember the radio messages warning them Ms Topic was experiencing mental health issues and there was no attempt to call in a mental health trained officer.

Mr Craddock questioned "whether the police officers were adequately trained to respond consistently with the information that had been conveyed" and whether mental health training was working in tandem with weapons practices.

Two of the three officers on the scene had taken part in a one-day mental health training program.

The court heard after Ms Topic's death a psychiatrist found she was probably suffering from an untreated psychosis; she had also previously been diagnosed as suffering ADHD, Asperger's and symptoms of autism.

Capsicum spray was used on Ms Topic but it was only after the Taser malfunctioned that she was fatally shot. (AAP) (AAP)

Mr Craddock said the only plausible explanation for her grabbing the knife that day was that she was afraid.

"There seems no realistically possibility Courtney wanted to harm anybody," he said.

Ms Topic's mother Leesa sobbed throughout the hearing.

In a statement to the court, the family said her death "was sudden, unexpected and violent".

They posed many questions centred around the police response and the wider issue of approaching people in disturbed states.