Convicted double murderer Mark Lundy says the case against him was possibly one of the most scientifically complicated yet argued in New Zealand – and too complex for a jury.

"I say that it is inappropriate and unrealistic to expect a jury to determine such complex issues of scientific dispute," appeal papers filed on behalf of Lundy say.

No date has been set for the hearing, but the Court of Appeal has allowed Fairfax NZ access to the notice of appeal filed for Lundy. The document begins his appeal against his conviction and sentence.

It says Lundy, 56, is now in Whanganui Prison and will be asking for a state-paid lawyer through the legal aid scheme.

At the end of his eight-week retrial on April 1, Lundy was found guilty in the High Court at Wellington of murdering his wife Christine and daughter Amber at the family's Palmerston North home on August 30, 2000.

The appeal intends to reopen a topic already challenged before the trial through the High Court and Court of Appeal.

Both courts said the evidence of messenger RNA, extracted from DNA, could be used in the trial, although the issue split the three Court of Appeal judges. One of the appeal judges sided with Lundy, saying the evidence lacked sufficient validation to be used in court.

The Supreme Court refused to hear an appeal at the time, noting that it was a point that could be raised again after the trial, if necessary.

Lundy's notice of appeal says evidence of messenger RNA will again be raised.

During the trial, the jury heard that it was believed only two countries used RNA evidence in court: New Zealand and the Netherlands. It was a Dutch expert who was the Crown's witness on the subject.

Laetitia Sijen said a smear of tissue found on Lundy's polo shirt was either brain or spinal cord tissue, more likely to have been human than any of the eight common farmed or pet species against which it was compared.

Lundy's lawyers called two witnesses on the topic. His appeal document said the witnesses, Stephen Bustin and Marielle Vennemann, were world leaders in their field and said messenger RNA was not yet ready to be used in court.

It was an area singled out in the trial judge's summing-up to the jury, and its complexity was indicated by the handout the judge prepared for the jury, Lundy said.

"It was crucial and central to the Crown case, and remains in real scientific dispute.

"I say that it is inappropriate and unrealistic to expect a jury to determine such complex issues of scientific dispute."

Lundy's notice of appeal said it was likely the appeal would raise other aspects of the evidence, including petrol consumption. At the trial it had been disputed how much petrol his car had used, and how much would have been needed to complete a return trip between Petone and Palmerston North if he killed his family as the Crown alleged.

Lundy was also considering arguing whether the verdicts were unreasonable in light of the other evidence, and the reliance the Crown put on science that was inherently unreliable.

Detailed submissions are yet to be filed. It was unlikely Lundy would ask for witnesses to give evidence at the appeal.

Lundy's lawyer for the appeal is Julie-Anne Kincade, who was also one of the lawyers for his trial.

The Privy Council in London ordered the retrial, after Lundy was found guilty at his first trial, held in Palmerston North in 2002.

He was freed on bail after the Privy Council decision in October 2013, and remained free until the end of the retrial.

When he was found guilty a second time, the judge immediately imposed life imprisonment with no chance of parole for at least 20 years. Taking into account the time already served, Lundy will first be considered for parole in August 2022.