A judge is expected to rule next week on a claim by Teina Pora that police are in breach of a court order directing them to provide information for his appeal over a 20-year-old rape and murder.
Pora's representatives sued the police last year and won an order for police to supply information held by the ESR. It is understood they claim police have not complied.
Pora wants access to the information for a bid to gain an appeal before the Privy Council.
Detective Superintendent Andy Lovelock said police had a view, but he was not prepared to comment.
Mr Lovelock said it was logical to retest exhibits from the case as DNA techniques improved.
Pora was twice convicted of the 1993 rape and murder of Susan Burdett. Malcolm Rewa, whose semen was found in her body, was convicted of her rape.
Rewa was convicted of sex attacks on 24 other women acting alone in all instances.
No physical evidence was found to indicate Pora was present.
Pora was convicted on the basis of a confession which a world expert on false confessions has described as "fundamentally flawed" and motivated in part by a $20,000 reward.
The view of Pora's team is that Rewa alone was responsible and that information held by the ESR may help to demonstrate that.
The case has divided police. The police's criminal profiler, whose expert evidence convicted Rewa of the other 24 cases, is among those who believes Rewa acted alone.
Rewa was convicted of raping Ms Burdett, but two juries could not decide on a murder charge.
Pora was convicted a second time in 2000 when the prosecution argued that Pora and Rewa acted with one or two other men.
But police did not make further inquiries for 10 years until private investigator Tim McKinnel began reviewing the case on behalf of Pora.
"The irony is their own expert has been telling them since 1996 there is no second or third offender - only Rewa," Mr McKinnel said.