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Credit: CBS Photo Archive/Getty; Alfred Eisenstaedt/The LIFE Picture Collection/Getty

Fifty-five years ago on Saturday, the world lost a luminous legend of the screen when Marilyn Monroe died at 36 on Aug. 5, 1962, of a barbiturate overdose.

Although Monroe’s death was officially ruled a “probable suicide” by the Los Angeles County coroner’s office, mystery has surrounded her untimely passing ever since, with some speculating that her alleged affairs with President John F. Kennedy and his brother Attorney General Robert F. Kennedy may have played a role.

Before she died, Monroe’s personal life was a shambles: Thrice divorced, she wasn’t a mother (her fondest wish), and many believe she had had, or was still having, affairs with both of the Kennedy brothers. It was reported that she had been threatening to hold a press conference divulging her relationships with them.

Rumors about Monroe’s alleged affair with JFK were spurred in part by her sultry “Happy Birthday” performance for the commander-in-chief at his 45th birthday celebration at Madison Square Garden on May 19, 1962, just months before the film star’s death.

A rare photo taken after the performance during a party at the home of movie executive Arthur Krim is reportedly the only known image of either Kennedy with Monroe.

Credit: Cecil Stoughton/The LIFE Images Collection/Getty Images

White House photographer Cecil Stoughton, who took the photo, kept it a secret for decades before releasing it in 2010.

“What happened to Marilyn Monroe is one of the great mysteries of the 20th century,” her biographer James Spada told PEOPLE in 2012, ahead of the 50th anniversary of Monroe’s death.

Though Spada doesn’t believe there’s any proof that the Kennedys were responsible for Monroe’s death, he said “it was pretty clear that Marilyn had had sexual relations with both Bobby and Jack.”

Robert F. Kennedy;John F. Kennedy
Credit: Ed Clark/The LIFE Picture Collection/Getty

According to Spada, actor Peter Lawford introduced Monroe to JFK in 1954. But when Kennedy tired of her, he passed her off to his brother. This happened, according to Spada, in the spring of 1962. And witnesses claim to have heard a disturbing tape, from the bugged Monroe home the night of her death, on which the voices of Lawford, an angry Bobby Kennedy and a screaming Monroe are audible.

During a 1983 BBC interview that Monroe biographer Anthony Summers conducted with the star’s former live-in housekeeper, Eunice Murray, he said there was a “moment where she put her head in her hands and said words to the effect of, ‘Oh, why do I have to keep covering this up?’ I said, ‘Covering what up, Mrs. Murray?’ She said, ‘Well of course Bobby Kennedy was there [on Aug. 4], and of course there was an affair with Bobby Kennedy.’ ”

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A so-called suicide squad was formed to investigate Monroe’s death. But according to Donald Wolfe, author of The Last Days of Marilyn Monroe, this squad never interviewed Murray, publicist Pat Newcomb, Lawford or any of the Kennedys. Biographer Summers said “both the forensic work and the police investigations were hopelessly flawed.”

Further fueling the theory that the Kennedys were involved in Monroe’s death is the fact that a couple of the people close to the investigation were later given high-profile new jobs. Publicist Pat Newcomb (who has never definitively spoken about Monroe’s death) “was spirited off to [the Kennedy compound in] Hyannis Port,” Michael Selsman, who worked for Monroe’s publicist, told PEOPLE in 2012. “Six months later she was awarded a job in the U.S. Information Agency in Washington, D.C.”

Spada told PEOPLE “there had to have been” a Kennedy-related cover-up, though not necessarily of murder.

“The Kennedys could not risk this coming out, because it could have brought down the President. But the cover-up that was designed to prevent anyone from finding out that Marilyn was involved intimately with the Kennedy family has been misinterpreted as a cover-up of their having murdered her,” he said.

In his 1997 book The Dark Side of Camelot, journalist Seymour Hersh wrote about the rumored affair between Monroe and JFK, saying the actress’ “instability posed a constant threat” to the president before she mysteriously overdosed.

Jerry Blaine, a former Secret Service agent in the Kennedy detail, told PEOPLE that he was with JFK during two known encounters the president had with Monroe — one at Lawford’s Santa Monica home in 1961, and another at the party in New York following the “Happy Birthday” performance.

“He probably thanked her for singing. But they weren’t alone,” said Blaine, who added that he “never saw any evidence of an affair … but I don’t know what happened behind closed doors.”

Monroe’s second husband, baseball great Joe DiMaggio, blamed the Kennedys for her death, according to Dr. Rock Positano, who along with brother John Positano wrote the 2017 biography Dinner with DiMaggio: Memories of an American Hero.

“ ‘The whole lot of Kennedys were lady-killers,’ ” DiMaggio told Positano, according to the book, ‘”and they always got away with it. They’ll be getting away with it a hundred years from now.’”

The baseball star added, ” ‘I always knew who killed her, but I didn’t want to start a revolution in this country. She told me someone would do her in, but I kept quiet.’ ”

DiMaggio also once told Positano of the Kennedys: “They did in my poor Marilyn. She didn’t know what hit her.”

Positano clarified DiMaggio’s statements in an exclusive interview with PEOPLE in May.

“The understanding was that her involvement with … the Kennedy clan put her in a position where maybe it wasn’t good for her mental health or her emotional health,” Positano said. “He didn’t think they were good people for her to be around.”