Crown lawyers have accused Mark Lundy's legal team of continually changing their story on the key evidence tying him to the murder, the two spots on his polo shirt.

As the Court of Appeal bid stretches into an extra third day, the Crown's team is now outlining its rebuttal to Lundy's reasons why he should be retried for the murders of wife Christine and daughter Amber in their Palmerston North home in August, 2000.

Crown lawyer Philip Morgan QC said the defence kept changing its tune on the spots found on Lundy's polo shirt, and the scientific analysis which found it was Christine's brain tissue.

"In 2002, the defence was 'here is Christine Lundy's brain tissue, but the police would have contaminated this inadvertently'.

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"And then they go to the Privy Council in 2013, and say 'you can't prove this was brain tissue'.

"At the [2015] trial they actually call witnesses to say that it is central nervous system tissue.

"And yet here we are again in 2017, and again there's an argument that we can't prove it's central nervous system tissue."

Morgan said several different pieces of evidence had been presented in 2015 by both the Crown and defence teams, which proved "absolutely and unequivocally" that the spots were brain tissue.

He said the spots couldn't have arrived on the polo shirt except by Lundy being at the murder scene at the time.

"The Crown case rested on proof that it was the deceased Christine Lundy's central nervous system tissue, which simply has to have been her brain, because it was her brain that had been exposed and found in various parts of the room," he told the court.

"The defence witness gave evidence that the small pieces of brain tissue, like this [found on the shirt] deteriorate quite quickly, becoming brittle and dry.

"You can't really smear them into clothes [afterwards]."

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In arguments made yesterday, Morgan said there was also plenty of evidence which showed the tissue was from Christine Lundy.

"Those two separate pieces of tissue, found in different places on the appellant's shirt, is the DNA of the deceased Christine Lundy. Not a trace, [but] high quality, high quantity. Again, uncontested.

"Those features demonstrated that this was the brain tissue of Christine Lundy. And the mRNA evidence, which was simply a part of the evidence, was simply one of the strands on which the Crown relied."

Lundy's legal team is basing most of its appeal on an mRNA analysis used to identify the spots as brain tissue, alleging it was unreliable science.

They also say the jury inappropriately tried to judge Lundy based on his demeanour in court, rather than on the evidence.

Finally, Lundy's lawyers want to present fresh evidence on petrol usage, that they say would show he wouldn't have had enough fuel to make the fatal trip to kill his family.

The appeal hearing is expected to finish today.