“A Bronx Tale: The New Musical,” Chazz Palminteri’s semi-autobiographical theatrical coming-of-age story, has been told and retold so many times that it has the ritualized feel of a folk myth — and not in a good way.

The author, not one to suppress childhood memories, first told about his conflicted Italian-American youth as an Off-Broadway solo in 1989, then Robert De Niro made his film directing debut with the 1993 movie, in which he played the father, after which Palminteri brought his one-man version to Broadway in 2007.

And now we have the musical, a by-the-numbers show written by Palminteri with similarities to “Jersey Boys” and “West Side Story” — but, again, not in a good way. De Niro is credited as making his Broadway musical directing debut here, although rumor and results suggest that his veteran co-director, Jerry Zaks, has done much of the heavy lifting.

Everything moves along at a professional pace on Beowulf Boritt’s picturesque mean-streets sets. The cast is fine, but seldom electrifying. Ersatz doo-wop is sung on the street corner by Palminteri’s alter-ego named Calogero (Bobby Conte Thornton), who also serves as narrator, announces for the first of too many times that “This is a Bronx tale,” and that it is his story. Once, at the start of the second act, he says “This is a Bronx tale,” then adds, as if anticipating audience impatience, “You know the story.”

For those who don’t, this is the tale of Calogero — nicknamed C by Sonny, the mob boss who takes him under his shark-suited wing. (The atypically routine costumes are by William Ivey Long.) In 1960, the boy is 9 years old and portrayed with an admirable minimum of show-biz pizzazz by Hudson Loverro.

In his neighborhood where, apparently, there are no other children, he learns the ropes from slick Sonny (a surprisingly restrained Nick Cordero) and pulls away from his honorable bus-driver father (Richard H. Blake). Eight years later, the conflict has intensified, complicated by territorial wars with the black neighbors.

Their singing is more Motown and, no kidding, they actually do have more rhythm than the Italian-Americans in Sergio Trujillo’s conventional choreography with the occasional aerial cartwheel. The familiar music by Alan Menken, Disney star composer, includes a paean to the Bronx stoop (“. . . on the stoop, stoop, stoop”). The lyrics by Glenn Slater (Menken’s collaborator on “The Little Mermaid”) have nursery rhymes you can anticipate before they are sung, many including the word “heart.”

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Finally, Calogero takes a last look back and says, “I think I am going to give the neighborhood a rest for a while.” An excellent, if unlikely, idea.