State Coroner John Cain found Constable Emmanuel Andrew's decision to fire a third and fatal shot at Gabriel Messo on July 16, 2020, was "gravely concerning".

In his findings into Mr Messo's death, Judge Cain said Const Andrew might have committed an indictable offence during the shooting.

The coroner on Thursday referred the matter to the Director of Public Prosecutions, saying homicide-related offences or conduct endangering life charges should be considered.

Mr Messo, who had diagnosed bipolar, was stabbing his mother Lilla in her head and neck with a stick at John Coutts Reserve when Const Andrew and another officer arrived.

Const Andrew ran ahead of his police partner and shot Mr Messo twice after the 30-year-old did not follow instructions to drop his weapon.

Judge Cain determined it was reasonable for Const Andrew to fire the first two shots as Mrs Messo was still being attacked.

But the third and final shot occurred five seconds after the second shot, when Mr Messo had already moved away from his mother and dropped his weapon, Judge Cain found.

The coroner was not satisfied Const Andrew used a reasonable amount of force or that he considered using pepper spray or a baton before drawing his gun.

Judge Cain was also critical of the lack of body-worn footage available as the two officers failed to activate their cameras.

He recommended Victoria Police review its processes and consider the feasibility of having cameras that automatically activate when a gun is drawn.

Chief Commissioner Shane Patton said Victoria Police would support Const Andrew while the DPP considered the coroner's findings.

"I am confident the DPP will assess the matter as quickly as possible given the length of time since the incident," he said in a statement.

AAP has contacted the Office of Public Prosecutions for comment.

Judge Cain also noted in his findings the lack of appropriate mental health care Mr Messo received.

The 30-year-old was brought to the Royal Melbourne Hospital under police guard the day before his death.

He appeared either drug-affected or in a psychotic episode when he was arrested after an incident at his aunt's house but was assessed as safe to be discharged.

Judge Cain found there were "clearly shortcomings" in Mr Messo's care at the emergency department.

The doctor who attended to him, Amelia Scharkie, did not access all the relevant files on his medical record.

But the coroner said even if Dr Scharkie were more experienced, it might not have made a difference.

Judge Cain noted Mr Messo and his family made repeated efforts to contact mental health services but the 30-year-old didn't receive the care he required.

The Messo family said it was clear the mental health system had failed.

"The family dearly hopes the coroner's recommendations and those of the royal commission continue to be implemented so that this never happens again," lawyer Jeremy King said on behalf of the Messo family.

Mrs Messo survived the attack but now lives with an acquired brain injury.

She was a very loving mother who continued to grieve her son, Mr King said.

The Police Association of Victoria maintained Const Andrew did his job to save the life of a vulnerable woman.

"You can't, two years later, slice and dice second by second, shot by shot, each and every action of these officers," chief executive Wayne Gatt told reporters.

"It's nonsense. We need to support them after these incidents, not condemn them."

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Australian Associated Press