Lawyers for Teina Pora have begun making their case at the Privy Council in London, saying the convicted murderer made a false confession to police because he suffers from significant brain damage.
Pora was paroled earlier this year after 21 years in prison for the 1992 rape and murder of Susan Burdett, of which he was twice convicted.
Overnight, lawyer Jonathan Krebs told the Privy Council his client suffers from fetal alcohol spectrum disorder and had a mental age of nine or 10 at the time of the crime.
Mr Krebs said extent and effect of the disability means Pora's confession should have been seen as unreliable.
"We are asking you to look at all of that material in the light of the scientific evidence now available which contextualises it and explains why the appellant would take the counter intuitive step of confessing to something that he did not do."
He said the 39-year-old's condition made him easily confused and meant he had a drive to please and satisfy others.
The Solicitor-General, Michael Heron, told the Privy Council that from the very beginning the veracity of the confessions has been the focus of the case, but Pora's confession was voluntary.
Mr Krebs showed to the Privy Council a police video that had been played at Pora's trial, which he said demonstrated his client got lost as he tried to take police to the crime scene.
He said the video showed police making a number of non-verbal clues to Pora as they drove around trying to find Ms Burdett's road and then her house.
Mr Heron said there were no clues given to Pora, who, he said, was able to describe many of the features of the crime scene, including a briefcase, a trophy and jewellery inside Ms Burdett's house.
Michael Heron said Pora described the briefcase and what was inside it. "How, realistically is it possible for him to have identified not only the briefcase in the next door room but its contents?"
Under questioning from Justice Kerr, Mr Heron confirmed Pora told police there were documents inside the brief case and he had rifled through them.
Mr Heron said Pora also described the light being on at Ms Burdett's home, the number of blows she received and some of the items inside Ms Burdett's home.
Mr Heron said there had been some media reports that had suggested impropriety on the part of the police but that was not the case.
"There is no suggestion of any moment that police or the prosecution have behaved improperly or unfairly."
Earlier, another lawyer for Pora, Ingrid Squire, looked at the evidence that links serial rapist Malcolm Rewa to the case.
Rewa has been convicted of 24 sexual attacks, including the one on Ms Burdett.
Ms Squire said Rewa had erectile dysfunction which would have embarrassed him and he would not have taken a younger man with him to offend.
She said said Rewa was known to use violence to subdue his victims and Ms Burdett's family and friends gave evidence that she would have fought back.
The appeal hearing before four justices and New Zealand's Chief Justice, Dame Sian Elias, has been set down for two days.
The Crown will continue its submissions at 11.30pm (NZ time) tonight.