“A Bronx Tale,” actor Chazz Palminteri’s autobiographical saga about growing up in an Italian-American Bronx neighborhood during the 1960s, amid organized crime and racial tensions, began as a one-man show performed in 1989. It was subsequently made into an acclaimed 1993 film starring Palminteri (who wrote the screenplay) and Robert De Niro (who directed).

Now De Niro and Palminteri have joined forces with Broadway director Jerry Zaks (the ’90s revival of “Guys and Dolls”), composer Alan Menken (“Little Shop of Horrors”), lyricist Glenn Slater (“School of Rock”) and choreographer Sergio Trujillo (“Jersey Boys”) to create a musical version of “A Bronx Tale,” which is receiving its world premiere at Paper Mill Playhouse in Millburn, New Jersey. De Niro serves as co-director and Palminteri wrote the book.

The musical, which resembles a combination of “Jersey Boys” and “West Side Story,” has a lot of promise (especially in Palminteri’s heartfelt storytelling and Menken’s early rock-style score), but it needs more work before it heads to New York or elsewhere.

Not much happens in the plodding Act One, except for setting up how the young Palminteri (Joshua Colley and Jason Gotay, both winning) is torn between his hardworking, law-abiding father (a sincere Richard H. Blake) and the slick local crime boss (a charismatic Nick Cordero). On the other hand, the choppy Act Two is an excess of tumult and plot twists.

Palminteri’s script relies too heavily on direct narration. At present, it feels less like a coherent musical than a one-man show paired with a doo-wop concert. But the production is polished and stylish, the score is catchy and Palminteri’s nostalgic air is touching. With further development, the Bronx may find a home on Broadway.