WINZ double-murderer Russell Tully appealing convictions, says he wasn't fit to stand trial

The man jailed for the 2014 murders of two Ashburton Work and Income employees is appealing his convictions and life sentence.

Russell Tully was jailed for a minimum of 27 years, but he claims Corrections misled the court about his mental fitness to stand trial.

He gave examples of psychosis, including a time he destroyed court documents while in prison.

"I ripped those books up, put noodles over it, and urinated over it," he told the Court of Appeal in Christchurch on Thursday.

He also claims to suffer from a "terminal" skin condition, which he treated daily.

His standby counsel Christopher Stevenson QC said the treatment Tully understood to be effective was hydrogen peroxide, which was administered directly into the ear canal.

But the Crown dismissed those issues as "delusional disorders".

"His skin condition is really irrelevant to his offending," Rebecca Thomson QC said.

"The fact of his believed impending death does not have any connection with the warped logic that led to his killing Ms Noble and Ms Cleveland."

In 2014, armed with a sawn-off shotgun, Tully shot dead Peggy Noble and Susan Leigh Cleveland, and injured Kim Adams inside the Work and Income New Zealand office.

"His actions were deliberate and calculated, as he hid his cellphone, disguised himself beneath a balaclava, then shot at the staff of the Ashburton WINZ office," Thomson said.

He'll now undergo genetic testing to assess whether his psychological issues are caused by a disorder.

Presiding Court of Appeal judge Justice Forrest Miller said "a possible bearing on sentence is about as high as you could put it".

The three judges have reserved their decision.