Woody Allen supplied the book based on the screenplay that he wrote with Douglas McGrath for the film “Bullets Over Broadway.” Set in 1929 New York City, the show uses well-known songs from the past instead of an original score. Susan Stroman has directed and choreographed with her trademark inventiveness and savvy.

The story involves David Shayne, an aspiring, idealistic playwright (Zach Braff); a gangster, Nick Valenti (Vincent Pastore), who puts up money for a Broadway production on condition that his untalented floozy girlfriend, Olive Neal (Heléne Yorke), acts in it; the fading one-time star Helen Sinclair (Marin Mazzie); the gluttonous actor Warner Purcell (Brooks Ashmanskas); Valenti’s right-hand thug Cheech (Nick Cordero), who takes to revising Shayne’s play, thereby making it a hit, and assorted other characters adding to the zany mix that director Stroman stirs with frequent hilarity.

There’s fun right from the start. The show’s title appears gradually splattered in the background with machine-gun fire. And when the chorus gals appear at Nick’s Club to the tune of “Tiger Rag” dressed in amusing costumes with tails wagging, we know we are in good hands. Using established music, a favorite pattern in Allen’s films, means no original score. But who could write an original score today that would match the assortment that includes “The Hot Dog Song;” “Up the Lazy River;” “I’m Sitting on Top of the World;” “Let’s Misbehave;” “(I’ll Be Glad When You’re Dead) You Rascal You;” “’Tain’t Nobody’s Business If I Do;” “Runnin’ Wild;” “There’s a New Day Comin’;” “There’ll Be Some Changes Made” “I’ve Found a New Baby;” “She’s Funny That Way” and more?

Braff is a perfect choice as the playwright overrun by what he is up against in moving to the Broadway scene from Pittsburgh. Mazzie, with her powerhouse voice and acting chops, is a whirlwind force as the egotistical star making her comeback and seducing the playwright. Ashmanskas is consistently funny gobbling up food wherever he can, including the dog biscuits that the amusing Karen Ziemba as actress Eden Brent, an actual cute little dog in hand, gives to her pet. Cordero is a show-stealer as Cheech, and Yorke is a delight giving the inept actress gal of the mobster boss a style of her own. She nails down voice and gestures that distinguish her portrayal from similar types and manages to be very, very funny until Cheech bumps her off, gangland style, for being such a lousy actress.

I also enjoyed the performance of Betsy Wolfe as Ellen, the playwright’s back-home girl whom he is ready to cast aside for his infatuation with Helen Sinclair. The book yields a surprise on that score when Ellen has her big moment, singing “I’ve Found a New Baby.” There is another good portrayal by Lenny Wolpe as Julian Marx, the ever-compromising agent.

Stroman’s choreography for the men playing gangsters is smart, and they, as well as the chorines, work very hard. The women dancers look great, whether garbed in fur for a number, or as train stewardesses dancing in front of or on top of a train bound for a New Haven tryout. Stroman has a stroke of genius with her dancing men garbed as hot dogs in buns for one big number. Santo Loquasto’s set designs are eye-catching and William Ivey Long’s costumes are great, whether for those sported by the chorus gals or the dazzling gowns worn by Mazzie. Everything clicks harmoniously.