What jury didn't hear in NT cop's trial

But on Friday the Supreme Court in Darwin lifted the non-publication order with Justice John Burns saying it was in the interest of open justice.

It was among 26 suppression orders revoked that included a ban on publishing Const Rolfe's text messages to his mates in the army.

The decision also permits the media to report that Const Rolfe's father, Richard Rolfe, was accused of intimidating a key prosecution witness during his son's trial.

The court heard on March 1 when the jury was not present that Mr Rolfe allegedly spoke to expert witness Senior Sergeant Andrew Barram in the toilet about his evidence and stared at him in an intimidating manner.

Mr Rolfe later denied it, saying to the NT News that the two had simply passed each other in the bathroom.

Const Rolfe's lawyer David Edwardson QC appealed to the court to leave in place three suppression orders related to the assault, the text messages and other evidence about his client's behaviour.

He said much of the material was misconceived allegations that had not been proven and it would be defamatory for his client and of little interest to the public.

Mr Edwardson said there were also future inquiries to consider, including the coronial inquest into Mr Walker's death, which has been scheduled for September 5 in Alice Springs Local Court.

But the prosecutor during Const Rolfe's murder trial, Philip Strickland SC, said a judge had made a finding against Const Rolfe, 30, including that he "deliberately assaulted" a man named Malcolm Ryder and lied about it when giving evidence.

Justice Burns said the risk that Const Rolfe's reputation could be damaged was less important than ensuring the public had the ability to scrutinise the court's decisions.

Const Rolfe was acquitted on all charges last Friday after a five-week trial over the shooting death of Mr Walker in November 2019 during a failed arrest in the Aboriginal community of Yuendumu, 290km northwest of Alice Springs.