Marc Chagall. “The Fiddler (Le violoniste),” 1912-1913. Collection Stedelijk Museum Amsterdam. (Collection Stedelijk Museum Amsterdam)

If Tevye the milkman had a ruble for every time someone connected “Fiddler on the Roof” to Marc Chagall, he would be a very rich man. Recent articles about the play’s 50th anniversary link the title to a Chagall painting —­ a claim that some theater Web sites echo.

The marriage between Chagall’s violinists soaring over shtetl chimneys and “Fiddler” seems to have been arranged celestially. But some of the contours of that union remain, as Tevye would say, as shaky as a fiddler on the roof.

Boris Aronson, who had collaborated with Chagall in Moscow theater, quoted the painter in his design of the first “Fiddler” set. And Jerry Robbins, who directed the play, recorded in his notes after reading the script in 1963, “In searching for a comparative vision, the paintings of Chagall came the closest,” says Alisa Solomon, author of “Wonder of Wonders: A Cultural History of Fiddler on the Roof.”

Despite consensus that ­“Fiddler” creators Jerry Bock, Sheldon Harnick and Joseph Stein had Chagall on the brain, there is some dispute about which Chagall works helped coin the title.

Chagall’s Wikipedia page finds in favor of his 1912 “Le Violoniste,” which is on long-term loan to Amsterdam’s Stedelijk Museum. That’s news to Geurt Imanse, who curates the Stedelijk’s fine arts collection.

“It depicts a fiddler more or less flying free in space. Only one of his feet is painted against the background of the roof of a tiny farmhouse, so one can hardly say the guy is standing on the roof,” Imanse notes.

The Guggenheim’s “Green Violinist” (1923-24), which similarly depicts a violinist hovering above roofs, is also cited as a precursor.

“The title of the musical does not refer to any specific painting,” Solomon says. “It was one option on a growing list of title possibilities the authors were considering.”

But the District’s Arena Stage, which will open a “Fiddler” production on Friday, states on its Web site that the play title “was inspired by a painting called ‘The Fiddler’ by Marc Chagall.”

Todd Rosenthal, who designed Arena’s set, did not remember which painting that was. His palette for the Arena production combines Chagall’s and Andrew Wyeth’s schemes, he says, noting the former’s “dark whimsy.”

Rosenthal and colleagues at Arena found no evidence that fiddlers actually played on shtetl rooftops. “We had a conversation about it. I think it’s more of an ethereal idea,” he says. “That’s how we are treating it —­ more of an allegory than an actual, physical person.”

Susan Goodman, senior curator emerita at New York’s Jewish Museum, points to the artist’s 1908 “Le Mort,” in the collection of Paris’ Musée d’Art Moderne, as an example of a work that shows a fiddler seated on the roof, rather than flying above.

“I was always led to believe that his grandfather or uncle was eccentric and often climbed to the roof to be alone,” Goodman says of Chagall.

Solomon has heard that fiddlers played funeral processions from rooftops in the shtetl. “I can’t verify that,” she says. “I didn’t put it in my book.”

Wecker is a freelance writer