You could make a documentary about Jewish ballplayers without interviewing Sandy Koufax.

But why would you? That was a question facing Peter Miller, the director and a producer of “Jews and Baseball: An American Love Story,” which will open in theaters in New York on Friday.

The problem facing Miller was that Koufax rarely agrees to be interviewed at length. For Jane Leavy’s 2002 biography, “Sandy Koufax: A Lefty’s Legacy,” Koufax verified facts and told friends they could speak to her, but there was no interview.

“His voice wasn’t absent,” she said. “I saw him on a golf course and at spring training with other people, and he didn’t impose any limitations.” More recently, Koufax also declined to speak to Leavy about Mickey Mantle, the subject of her new biography.

Miller recognized that getting Koufax to speak would be a coup — he knew through archival footage dating to the pitcher’s days as a Brooklyn and Los Angeles Dodger that he “had a great wit and there was always a little twinkle in his eye.” Unlike the other towering figure in Jewish baseball history, Hank Greenberg, Miller said, “Sandy’s around and articulate and beautiful to look at.”

Koufax consented to participate after receiving a letter from Ira Berkow, a former New York Times sports columnist, who wrote the script for the film. “I wanted to emphasize to him that it would be an important documentary,” said Berkow, who had interviewed Koufax in the past. A couple of weeks later, Berkow said: “I got a call. He said, ‘Hi, it’s Sandy.’ ”

According to Berkow, their conversation concluded when Koufax said, “It doesn’t make sense if it’s ‘Jews and Baseball,’ and I’m not in it.” Berkow added, “I said, ‘I can’t disagree with you.’ ”

Koufax gave two interviews to Miller, each at the director’s apartment in Manhattan.

“He didn’t speak for long in the first one and was pretty reserved,” Miller said. “We rode down in the elevator, we chatted about a number of things, and he said: ‘I don’t think that went so well. I’ll give you a call,’ and a few days later, he phoned back. He said, ‘Hi, it’s Sandy, we should do it again.’ ”

In a dark jacket, shirt and tie, the silver-haired Koufax spoke with charm, wit and a bit of candor about his career and his decision never to pitch on Yom Kippur, most notably in Game 1 of the 1965 World Series. Not playing on Yom Kippur and Rosh Hashana was “just something I’d always done out of respect,” Koufax told Miller, “but I could always do something about it; there was always a game the day before, so I’d move up and pitch on two days’ rest so I wouldn’t miss a start at the end of the season.”

But, Koufax continued, “there was no game the day before” Game 1, which the Dodgers lost, 8-2.

When the starter Don Drysdale was knocked out of the game in the third inning, he told Dodgers Manager Walter Alston a version of this wisecrack: “I bet right now you wish I was Jewish, too.”

Koufax and Drysdale’s joint holdout before the 1966 season was viewed by Marvin Miller, the new leader of the players union, as an important early step in strengthening labor’s hand. Koufax said in the film, “Since there was no such thing as free agency, you went in and you talked to the general manager and you tried to negotiate, which meant they threw you a crumb and you went home.”

Peter Miller said that Koufax, who was accompanied by his wife, Jane, at each interview session, “seemed to be saying, ‘I need to tell the story,’ and he was giving and willing to do it.”

The last time Koufax spoke to a national network was in 1999, when he gave an hourlong interview to ESPN for the “SportsCentury” series chapter on him. But HBO, which specializes in sports documentaries, has been turned down by Koufax several times over the past 30 years.

“Jews and Baseball” focuses on more than Koufax and Greenberg. It goes back to Barney Pelty, called the Yiddish Curver; Mose Solomon, the so-called Rabbi of Swat; and other Jewish players like Moe Berg, Al Rosen, Buddy Myer, Marv Rotblatt and Kevin Youkilis. But the 90-minute film will probably be best remembered for the extended star turn by Koufax, 44 years after his last pitch.