Police have been criticised, but cleared, over their handling of the man who killed Auckland jogger Jo Pert.

The Independent Police Conduct Authority said today police officers should have made more enquiries when dealing with Tevita Filo on January 6.

They also found a police dispatcher did not pass on all the available information.

Filo killed Pert as she jogged on Shore Rd, Remuera the following morning but the authority said it was not possible to draw any link between her death and police actions the day before.

A family member and an ex-policeman who was a close friend of Pert both complained to the authority about how police handled Filo the night before the murder.

Filo was not arrested on January 6, despite being found stalking a couple and with a large knife in his possession.

Justice Murray Gilbert found Filo not guilty by reason of insanity for her murder and of 12 other alleged crimes in the 17 hours before and after her death, because he was incapable of understanding his actions were morally wrong due to his schizophrenia.

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

Detective Inspector Kevin Hooper last year 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."

Hooper said they issued a roadside warning.

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