Morrison, Greens senator Sarah Hanson-Young and Labor’s Penny Wong were sent a letter detailing a complaint last week about an alleged rape which occurred when the woman was 16.

The Adelaide woman went to NSW police last year, but the investigation was suspended when she took her own life in Adelaide in June 2020 after telling authorities she didn’t want to proceed.

The strike force established to investigate the claims confirmed on Tuesday the matter was now closed after reviewing a document thought to be the woman’s diary.

“NSW Police have since sought legal advice in relation to these matters,” police said in a statement.

“Based on information provided to NSW Police, there is insufficient admissible evidence to proceed.”

The prime minister has said he’s spoken to his minister about the issue, saying: “The individual involved here has vigorously rejected these allegations… it’s a matter for the police.”

“At this stage, the commissioner has raised no issue with me – and the (prime minister’s) department secretary was present for that call as well – that would cause me to take action under the ministerial code,” Morrison said.

Morrison said “distressing” issues had been raised, but the proper action was for police to deal with them.

“That’s how our country operates. That system protects all Australians.”

But Turnbull called for the man to come forward and explain what dealings he had with the woman, including when he knew of the complaint.

“He should out himself and he should provide a comprehensive statement about what he knows about the allegations,” he told ABC radio on Tuesday.

“If he’s vigorously denied the accusations to the prime minister, he should vigorously deny them to the public.”

Turnbull said it would be “impossible for him to function in that cabinet”.

“Are we seriously going to have a Question Time where the opposition asks every single minister whether they are the person named in the complaint?”

The former Liberal prime minister launched a sharp critique of his successor’s approach.

“It’s not good enough for the prime minister to say it’s a matter for the police,” Turnbull said.

“The prime minister cannot outsource his responsibility for composing his ministry to the police.”

Turnbull, who exchanged correspondence with the woman in 2019 about her allegations, is calling for a coronial inquest into her death.

He said he had a “question mark” over her death because it coincided with the release of explosive sexual harassment allegations against former High Court judge Dyson Heydon.

“If she did suicide, if she did take her own life, what led to it?”

“Why did she suicide? Why did she pursue this complaint for so long and then, just at a moment when you think she’d be encouraged, take her own life?”

The Greens want the minister to stand aside pending an independent investigation by a former judge, given the woman’s death poses a significant roadblock for a police investigation.

“Sitting around that table erodes the trust the integrity and belief that this government takes sexual assault seriously,” Greens Senator Sarah Hanson Young said, and raised the possibility of the minister’s name being brought up in parliament when it resumes on March 15.

“There is of course always the avenue of using parliamentary privilege,” she told ABC’s 7:30.

“It’s open for any member of the parliament to stand up and call this out when parliament resumes – I don’t think the Prime Minister should wait for that.”

South Australia Police are now preparing a report on the woman’s death for the coroner.

Premier Steven Marshall said it is “quite possible” the coroner will conduct an inquest into the death, and expressed his support for a police investigation into the matter.

“I think that the appropriate way to proceed is for the police to conduct their investigation, and I strongly support that,” Marshall said.

“In terms of whether the coroner should do an inquest in South Australia, it’s quite possible the coroner will conduct an inquest into the death, but that really – under our statute – can’t begin until the police investigation has concluded.

“But that would be a matter for the coroner.”

Marque Lawyers, which represented the woman when she took the complaint to police, used Twitter to query the prime minister’s comments.

“It is surprising to hear the prime minister say that he hasn’t read the detailed written allegation of sexual assault of a child, made against a senior member of his cabinet, but only been ‘briefed’ on it,” the firm said.

The lawyers also questioned why the prime minister had accepted the minister’s denial at face value without investigating further.

-with AAP