No mere documentary can capture the turbulent life story of “America’s mayor.”

In order to do justice to the rise and fall of Rudolph “Rudy” Giuliani, director Jed Rothstein had to invent a new genre. The result, “Rudy! A Documusical,” weaves in musical performances by Broadway actors with archival footage from Giuliani’s metamorphosis from top prosecutor to New York City mayor and hero of 9/11 to his sad final act as Donald Trump’s cable news henchman and chief purveyor of election lies.

“Rudy is this very unique and mercurial character,” says Rothstein. “He’s very operatic. His personal story is like an opera with these cartoonishly extravagant highs and lows.”

But staging a full-on opera would have been too costly and time consuming for the filmmakers, so Rothstein turned to another Big Apple staple — musical theater. The numbers themselves were written and performed to delineate key turning points in Giuliani’s life and career.

“The songs add an important emotional perspective to a story of a person who has lived in the public eye for a long time and help us better understand why he did what he did,” says Rothstein.

In the documentary, which premieres Thursday at the Tribeca Festival, Rothstein talks to political reporters such as Olivia Nuzzi, as well as Giuliani’s friends and associates like former New York City Police Commissioner Bill Bratton and retired detective and media personality Bo Dietl. But Giuliani turned down multiple interview requests.

“I’d love to have asked him what he thinks his legacy will be,” Rothstein says.

The director, who also helmed “WeWork: Or The Making and Breaking of a $47 Billion Unicorn,” says he wasn’t interested in doing a hit job on Giuliani. But the film does probe the more sordid parts of the mayor’s legacy. They include his peddling of lies that the 2020 presidential election was stolen (a falsehood that helped lead to the Jan. 6 riot), along with his shady dealings in Ukraine, which inspired the first of Trump’s impeachments. That’s to say nothing of Giuliani’s willingness to cozy up to strongmen and dictators in return for big paydays, a mercenary brand of globe-trotting that enabled the mayor to cash in on his 9/11 halo.

“The people that knew him best and knew him longest, say that after 9/11 he had a choice to go high or go low,” says Rothstein. “For many years he was a public servant, living on a public servant’s salary. But after he re-married [third wife] Judith Nathan, they got a taste of the high life. They got a taste of owning houses in the Hamptons and Palm Beach and traveling on private jets. Once he made making money the yardstick of success, that’s when he became a cautionary tale.”

And Rothstein also doesn’t shy away from examining the way that Giuliani’s crackdown on crime as mayor led to policies like stop-and-frisk, which exacerbated racial tensions.

“People always talk about how Rudy cleaned up Times Square,” says Rothstein. “Well, that’s the perspective of white people, but I think people of color had a very different experience of his mayorality.”

That’s not to say that Giuliani failed to rise to the occasion when his city and his country needed him the most. “Rudy! A Documusical” follows the mayor in the midst of 9/11, capturing him as he runs through lower Manhattan in the moments before the Twin Towers collapse. It also reminds viewers of the compassion he showed to the families of the victims of the terrorist attack, particularly to the loved ones of rescue workers, police and firemen who died trying to help people.

“People are complicated,” says Rothstein. “Rudy is capable of good and bad things. He had a clear sense of leadership and he had a clear mastery of the city. When 9/11 happened, he rose to the occasion. He was the right man for that moment.”