Here’s why Roman Polanski thought Bruce Lee killed Sharon Tate

In 1969, Bruce Lee — made famous a few years before for the TV show “The Green Hornet” — was Hollywood’s martial-arts instructor of choice. Roman Polanski, Steve McQueen and celebrity hairdresser Jay Sebring were his students. Lee even tutored It-girl Sharon Tate for her movie “The Wrecking Crew.”

But that summer, the actor, then 29, played a shocking role: Polanski briefly considered him a suspect in the murders of Tate, Sebring and others — killings eventually tied to Charles Manson and his followers.

That era is captured in Quentin Tarantino’s “Once Upon a Time in Hollywood,” in theaters Friday.

Leonardo DiCaprio stars as an actor living next door to Tate and Polanski who, along with a stuntman played by Brad Pitt, encounters the Manson family — and Lee (Mike Moh).

In real life, Lee’s introduction to the glittery crowd began with a Southern California kung-fu demonstration in 1967. Martial-arts enthusiast Sebring was in the audience and wowed by Lee. Already established in Hong Kong fight flicks, Lee — who was born in San Francisco but raised in the then-British colony — hoped to make it in Hollywood. Sebring showed the footage of the demo to producer William Dozier, who went on to cast Lee in the 1966 ABC series “The Green Hornet.”

Sebring had stayed close to his ex-girlfriend Tate. According to the book “Bruce Lee: A Life,” by Matthew Polly, Tate invited Lee over for dinner and correctly predicted that he and her director-husband Polanski would “get along like a house on fire.” The two became pals as well as kung-fu mentor and student — and Lee would later be a support to ­Polanski after Tate’s murder.

That, of course, happened on Aug. 9, 1969, at the couple’s home at 10050 Cielo Drive in Los Angeles.

Polanski was researching a project in London when Tate, Sebring, writer Voytek Frykowski and coffee heiress Abigail Folger were brutally killed.

While police were initially clueless, Tate and Polanski’s friends had plenty of theories about who had committed the crime. Filmmaker Andrzej Krakowski, a friend of Polanski’s who identified the bodies, told The Post he initially suspected gun-loving Fry­kowski in a murder-suicide scenario. Others blamed the Mafia or drug dealers. Krakowski also recalled that Paul Tate — Sharon’s father and a former Army intelligence officer — adopted a hippie-ish look and frequented Sunset Strip bars where chatty scenesters might know something.

Polanski, meanwhile, believed it was an inside job, according to Christopher Sandford, author of “Polanski: A Biography.” Aiming to solve the crime, the director would wander late at night through LA’s ritzy neighborhoods — sneaking into friends’ driveways and hunting for blood on their Porsches and Lamborghinis. He spent $2,500 to analyze producer William Castle’s handwriting, seeing if it matched the bloody lettering of “Pig” left by the killers on his front door. It didn’t.

“Polanski fancied himself as a detective manqué,” said Sandford.

When he discovered the prescription for a pair of glasses found at the crime scene, the director obtained a pricy lens-measuring gauge. For months, he surreptitiously checked friends’ prescriptions to see if they matched, Sandford said.

Shortly after the murders, Lee was training Polanski in the Paramount Studios gym when he mentioned that he had recently lost his glasses and needed to replace them.

“It doesn’t surprise me that Roman came to the conclusion [that Lee might have committed the murders],” said Krakowski. “Anyone who wore glasses would have been a suspect to Roman.”

According to Polly, Polanski set into motion a potential trap. “Very coolly, Polanski said to Bruce, ‘On the way home, we can stop at my ophthalmologist for glasses. It will be my gift to you.’ Much to Polanski’s relief … the prescriptions did not match.”

By Dec. 1, 1969, Manson and five followers were arrested in connection to the murders. All were found guilty and sentenced to death (commuted to life in prison after California abolished the death penalty).

Perhaps out of guilt, Polanski later picked up the tab for Lee to join him in Gstaad, Switzerland. Officially, the actor was there as Polanski’s trainer, earning $10,000. Unofficially, it was a busman’s holiday for Lee — who complained of being bored with all the skiing and cocktailing.

“Bruce was a terrible skier and he borrowed a jumpsuit from Polanski,” said Polly. “It was the inspiration for his yellow jumpsuit in ‘Game of Death’ [the film that Lee died while making in 1973] — and that served as a model for the outfit worn by Uma Thurman in [the 2003 Tarantino movie] ‘Kill Bill.’ ”

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