Did a conspiracy by U.S. State Department officials and art dealers secure a prize for painting for Robert Rauschenberg at the Venice Biennale in 1964?

Unconfirmed rumors of some sort of nefarious plot to that effect swirled in international art circles for years.

The documentary filmmaker Amei Wallach had heard them, and she was curious to know if they held any truth.

“This moment is a kind of urban legend in the art world,” said Wallach in a telephone interview from her home in New York on Long Island. “It was a flashpoint. The story goes: The Biennale had been a Eurocentric party, and this was the first time an outsider broke the code.”

Using archival footage and interviews with important figures involved in the 1964 Biennale, Wallach, the longtime chief art critic for Newsday and an occasional contributor to The New York Times, tried to unravel the mystery, exploring the charged political atmosphere that engendered those persistent claims.

The result is Zeitgeist Films’ “Taking Venice,” which will have its theatrical release next month in New York and Los Angeles.

The film revisits the Biennale and recreates the scene in which Rauschenberg’s artworks were brought through the Grand Canal by boat to get to the U.S. Pavilion in the Giardini, just in time to qualify for the award.

It also includes shots of the American art delegation flying into Venice in a U.S. military cargo plane filled with monumental Pop Art, and the opening party at the U.S. Consulate.

Wallach interviewed the leader of the 1964 Biennale team, Alice Denney, a Washington insider, who worked with the curator Alan Solomon and the art dealer Leo Castelli to bring Rauschenberg to victory.

“We didn’t cheat,” Denney said in the film, while conceding that a United States agency established to promote American dominance during the Cold War organized the art exhibition with an explicitly political agenda, to ensure that the show would reflect the United States well on the global stage. “We thought with Rauschenberg we had a very good chance.”

“One of the intriguing subplots of the Biennale all through the decades, more than a century, is how art and politics overlap,” said Philip Rylands, former director of the Peggy Guggenheim Collection in Venice, in the film. “There’s a kind of high altitude moment with the American presence in 1964. It reverberates through history.”

Placing the story in the broader context of 1960s social and political upheaval, the film also explores how the arms race between the United States and the Soviet Union had a corollary in the realm of culture — American diplomats felt that the “soft power” of art could help promote American ideological dominance against the Soviets.

Rauschenberg wasn’t quite an expression of apple pie and baseball. He had shaken the New York art world during his 1963 retrospective at the Jewish Museum, with his unclassifiable “Combines,” which tacked found objects onto canvasses with abstract brushwork. Some critics simply labeled it garbage.

“I was considered a clown by nearly everyone else,” the artist said in the film.

Solomon, the curator who organized the Jewish Museum show, felt sure Rauschenberg could win the Biennale’s grand prize for painting for his large silk-screen works and for “Combines.”

While his ultimate win was a coup for the American art scene — signaling a shift of the center of contemporary art from Paris to New York — the results were more complicated for Rauschenberg himself.

Interviewed some years after the Biennale, Rauschenberg reflected, “I had moments where I thought, everything would be much better if I hadn’t been so lucky.”

“Taking Venice” will premiere on May 17 at IFC Center in New York City and on May 24 at Laemmle Theaters in Los Angeles.