A mentally ill man who was shot by police at a busy shopping centre was granted day release from a mental health facility, despite allegedly telling his nurses and doctors he wanted to kill police.

Jerry Sourian, 23, was shot three times on Thursday afternoon after he was seen wandering around Westfield Hornsby's forecourt, dazed and carrying a large carving knife.

Two officers, a male and female, opened fire at Mr Sourian as he allegedly ran at the female officer with the knife.

Three female bystanders, aged 60 to 82, were hit by police bullets or bullet fragments.

NSW Health launched a review on Thursday into the circumstances surrounding Mr Sourian's release from Hornsby Hospital's Adult Mental Health Unit, where he had been admitted involuntarily in recent weeks due to schizophrenia.

Mr Sourian's family were distraught and questioned why police didn't use their Tasers when they confronted him staggering through the forecourt wearing tracksuit pants and no shoes.

"That's the simple question anyone would ask," one family member said. "It's just not right. The whole picture is ugly."

Fairfax Media can reveal that a senior doctor at Hornsby Hospital overruled the advice of other doctors and allowed Mr Sourian to leave for one hour a day.

This was despite a doctor's report that said Mr Sourian had expressed homicidal tendencies towards police and shouldn't be released.

Mr Sourian also absconded during day release last week and somehow flew to Melbourne. He was brought back to the mental health facility but was again granted day release.

On Wednesday, as he was leaving the hospital for his approved hour of leave, he had a heated argument with three family members.

His family ran back inside to seek help and a clinical aggressive response team was activated at 11.57am.

But by the time security arrived at 12.05pm, Mr Sourian had disappeared.

There were only two security staff on duty and they were at the other side of the hospital when the alert was raised.

For more than five years, security guards at Hornsby Hospital have been asking for more staff.

The Health Services Union has been calling for a dedicated mental health security presence at the hospital. Had one been working, Mr Sourian might have been prevented from leaving.

"Having only two staff on for a major metropolitan hospital with seven mental health units is just untenable," said Nathan Sing, a Health Services Union delegate and security guard at Hornsby Hospital. "We desperately need more staff."

A spokeswoman for NSW Health said almost all patients who were admitted involuntarily had a "graduated leave process prior to departure".

"Graduated leave from inpatient facilities is an important part of the inpatient therapeutic process," she said.

"Leave is granted on the basis of clinical and risk assessment, informed by a number of factors, including past history, information from carers, and clinical presentation."

HSU NSW Secretary Gerard Hayes said the state government promised a root-and-branch review of hospital security after an incident in Nepean Hospital's emergency ward this year.

In that incident, a police officer and security guard were almost shot dead by a patient on ice.

"We have seen no substantive increase in hospital security, just bureaucratic waffle and inertia," he told Fairfax Media on Friday.

The NSW Health spokeswoman said a 12-point security plan announced after the Nepean incident was "progressing".

This included better training for security guards and recruiting additional staff.

Hornsby Hospital did not respond to questions about staffing levels.

Update: A NSW Health spokeswoman has denied Mr Sourian had threatened to harm police or that a consulting psychologist overruled advice not to allow day release. 

"All treatment decisions were made by the patient's treating psychiatrist and the decision for him to be allowed an hour's leave with his family in the grounds of the hospital was made by that psychiatrist in consultation with the family," the spokeswoman said.