Judges have retired to consider the Ashburton Work and Income killer's bid for a reduced sentence.
The shooter has taken his case to the Court of Appeal in Christchurch.
54-year-old Russel Tully has asked the court to take the results of his chromosomal test into account.
Crown lawyer Rebecca Thomson QC said while the chromosomal disorder Tully suspects he has is associated with a range of psychological issues, whether his personality issues are genetic is irrelevant.
"His interactions with WINZ weren't to do with his skin condition beliefs, but his sense of entitlement."
Presiding Justice Forrest Miller has agreed to allow a reasonable amount of time for the tests, before making a decision.
He said it could have a possible bearing on Tully's sentence.
In 2016, Tully was jailed for life with a minimum non-parole period of 27 years.
Justice Cameron Mander described the shootings at the time as "cold-blooded executions" by a "very dangerous person" capable of extremely violent actions.
Tully was found guilty of being the masked gunman who stormed the Mid-Canterbury Winz centre on September 1, 2014.
He was only in the building for 60 seconds – but in that time he shot dead 67-year-old receptionist Peggy Noble at pointblank range, and shot 55-year-old case manager Susan Cleveland three times as she pleaded for her life.
Tully was also found guilty of attempting to murder case manager Kim Adams, who felt a bullet whiz past her head.
He was found not guilty of attempting to murder case manager Lindy Curtis, who was shot in the leg and badly injured while hiding under a desk.
Tully is representing himself in court today, supported by amicus curiae - friend of the court - Christopher Stevenson, QC.
Tully's demeanour is much calmer than previous court appearances, during one of which he had to be removed from court and restrained in a wheelchair.
Today he's sitting quietly at the bench with Corrections staff, looking through banana boxes of extensive notes and paperwork he has prepared.
Stevenson is questioning Tully's amicus curiae at his original trial, James Rapley, QC, who is being asked about his interactions with the defendant at the time, and whether he believes Tully was able to fully participate in the trial.
Rapley has told the court Tully spent much of the time leading up to the trial fretting about a skin condition he believes he has, which he treats by pouring hydrogen peroxide into his ear canals.
The court heard Tully told lawyers he believed he only had two years to live, and would die in jail.
Rapley confirmed Tully was preoccupied in meetings about how he didn't have time to prepare for his trial, because it took him five hours a day to treat his condition.
He also confirmed Tully was not able to be present for a majority of the trial, and claimed he couldn't hear the evidence because his ears were in so much pain.
"At one stage, Tully was simply lying under a blanket moaning as the trial continued downstairs."
Tully has argued he wasn't physically or mentally fit to stand trial, and believes he may have an extra chromosome.
The gunman has now questioned Rapley and made his own submission to the Court.
Tully asked Rapley why he never sought a specialist medical opinion on his reported condition.
"The skin is the biggest organ in the body, it's made up of multiple layers. Did you ever consider sending me for further testing?"
Rapley said he didn't think further testing was needed.
But Tully argued almost all of his medical reports were done by primary care specialists – and one microbiologist who only gave him a cursory look-over.
Tully also asked Rapley whether he thought he suffered any neuroses.
"I certainly saw you had certain personality features… I didn't feel that you couldn't pay attention, understand or talk. I've dealt with clients who were in that space, who didn't even know who I was."
Tully gave evidence he was in ongoing mental distress in his management unit at Christchurch Men's Prison.
"I received some documents from the court and I actually destroyed those documents.
"I thought the black redacted lines were evil, so I ripped them up, put noodles on them and urinated on them."
Tully mentioned having a test done on his skin, which an expert told him looked as though he could have an extra Y chromosome.
Presiding Justice Forrest Miller said there's now funding for a DNA profile to test this.
Current amicus curiae Stevenson has argued Tully was given incorrect advice he couldn't plead insanity.
He's received an additional psychological report, which suggests the intensity of Tully's belief in his skin condition indicates a disease of the mind.
"Much of what was considered obstructive behaviour [in his trial] could've been indignation his condition was being regarded as psychological.
"His fixed and unshakeable belief of a skin condition making its way to the brain would've obstructed meaningful participation in the trial."
The right to be present extends to being psychologically there as well as physically, Stevenson said.
However, Crown lawyer Rebecca Thomson QC rejects arguments Tully was insane – and said his skin condition is irrelevant to his offending.
"All the psychologists say he has a challenging personality, but he was not insane in a relevant sense at the time of the offending."
Thomson acknowledged psychological reports say it is possible he suffers antisocial or narcissistic personality disorder, but she said neither doctor had enough information about his past to diagnose him.
Tully has so far only been diagnosed with somatic delusional disorder – centred on his supposed disease.
But he rejects this diagnosis, Thomson said.
"There's clear evidence when he went there that day, he knew what he was doing was morally wrong.
"He hid his cellphone… wore a balaclava… made a getaway on his bicycle while evading attempts by people to stop him – and even exchanged it for another bicycle hidden nearby. He also disposed of his shotgun."