One complaint has been laid against police for the handling of the Jo Pert murder case, and another is imminent.

The police watchdog, the Independent Police Conduct Authority, confirmed it has received a complaint regarding the case.

It is understood the complaint was laid by a member of the Pert family and centres around the mother of two's killer, Tevita Mafi Filo, not being arrested the night before her death, despite being found stalking a couple and with a large knife in his possession.

IPCA general manager Warren Young confirmed a complaint had been received.

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"We have received a complaint and we are looking at it to determine the next steps," he said.

Young said he was unable to clarify the nature of the complaint, but Fairfax reported that it was laid by a family member.

"It is inconceivable that in these circumstances, police did not exercise their discretion and take steps available to them to remove him from the community until a proper assessment of his risk could be made," the Pert family member told Fairfax.

Pert's father Kevin Pert told the Herald he had no idea a complaint had been made.

He said his family were very happy with the police investigation into her death.

A source told the Herald that another complaint was also being prepared.

Pert was killed on Shore Rd, Remuera as she went for a morning jog.

Filo was found not guilty by reason of insanity for her murder and also 12 other crimes alleged to have occurred in the 17 hours before and after her death.

Tevita Mafi Filo was found not guilty by reason of insanity for Jo Pert's murder. Photo / Michael Craig
Tevita Mafi Filo was found not guilty by reason of insanity for Jo Pert's murder. Photo / Michael Craig

The charges include following a couple in their car from St Heliers to East Tamaki on January 6.

Detective Inspector Kevin Hooper told media the decision by those officers to not take him into custody was the right one.

"Police confiscated the [weapon] at the time and officers questioned him at length. They checked the police computer to see whether or not there were any alerts against his name. As we know now there were no alerts that Filo had any mental health issues or that he posed any danger to the public."

Hopper said based on the officers' assessment of the situation, they used their discretion and issued a roadside warning.

The next morning, he killed Pert because he believed he was following orders to get back to the "real world".

Justice Murray Gilbert found him not guilty by reason of insanity because he was incapable of understanding his actions were morally wrong due to his schizophrenia.