The accusation has created a cloud over the 16 men in Morrison’s 22-minister Cabinet and is feeding complaints of a culture within Parliament that is toxic for women.
His conservative coalition has a smaller proportion of female lawmakers than other parties and has been accused of sexism.
The rape allegation was contained in an anonymous letter sent to the prime minister’s office and to three female lawmakers last week.
The 31-page letter contained a statement from a complainant, taken by her lawyer, that detailed her allegation of a rape she said occurred in Sydney in 1988. The minister had not been elected to Parliament at the time.
The letter, which included excerpts from her diary and a photograph from 1988, was forwarded by the lawmakers and Morrison to police.
The woman, who has not been named, took her own life in her hometown of Adelaide in June at the age of 49.
Morrison on Monday rejected calls to stand the minister down and to establish an inquiry, saying police should investigate.
But police said in a statement on Tuesday that “there is insufficient admissible evidence to proceed.”
The woman had asked for advice from South Australia state police in Adelaide about reporting her allegation in November 2019.
New South Wales police had been in charge of the investigation since February last year.
“For various reasons, the woman did not detail her allegations in a formal statement to NSW police,” the statement said.
Treasurer Josh Frydenberg, Morrison’s deputy in the then-ruling conservative Liberal Party, had been among government lawmakers who called for the accused minister to be allowed the presumption of innocence while police investigated.
Morrison said the minister “vigorously and completely denied the allegations.”
But the woman’s lawyer, Michael Bradley, and several critics of the government have called for the minister to step down while an independent inquiry investigates the evidence.
New South Wales Council of Civil Liberties President Pauline Wright described referring the issue to police as “nothing short of an abrogation” of Morrison’s responsibility for proper governance.
The accused minister is also under mounting pressure to make his own identity public.
The minor Greens party has left open the option of naming the minister under the legal protection of parliamentary privilege when Parliament resumes on March 15.
The contentious privilege, common in British Commonwealth legislatures, prevents lawmakers from being sued or prosecuted for anything they say in Parliament. The legal immunity also extends to media that report the lawmakers’ words.
Former Prime Minister Malcolm Turnbull, whom Morrison replaced in a power struggle within the government in 2018, has called on the minister to be identified and removed from office.
Turnbull said the complainant wrote to him in 2019 seeking advice on what she should do with her allegation.
“He should out himself and he should provide a comprehensive statement about what he knows about the allegations,” Turnbull told Australian Broadcasting Corp. “If he’s vigorously denied the accusations to the prime minister, he should vigorously deny them to the public.”
The police decision to drop the investigation comes two weeks after Morrison apologized in Parliament to a former government staffer who alleged she was raped by a more senior colleague in a minister’s office two years ago.
Brittany Higgins quit her job in January and reactivated her complaint to police after initially not pursuing the case because she felt it would have affected her employment.
The colleague, who has not been named publicly, was fired for breaching security by taking Higgins into a minister’s Parliament House office following a night of heavy drinking.
The Associated Press does not usually identify alleged victims of sexual assault, but Higgins has chosen to identify herself in the media.
The public disclosure has triggered a flurry of complaints about the behavior of lawmakers and a toxic work culture within Parliament House.
Australian Federal Police Commissioner Reece Kershaw told Sydney Radio 2GB on Tuesday that the man whom Higgins accused of rape would be contacted by police “at the appropriate time.”
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