For Stroman, dancing is a turbocharged form of acting. That philosophy has helped her to become the top choreographer in American theater, winning two Tony awards (for the 1992 “Crazy for You” and the 1994 “Show Boat”). And there may be one or two more Tonys coming for her direction and choreography of “Contact,” a runaway hit this season (it has just moved from Lincoln Center’s Mitzi Newhouse Theater to its bigger main stage, the Vivian Beaumont). The three sections of the show, written by John Weidman, make up a triptych on the varieties of human connection and disconnection. The first piece, “Swinging,” takes Fragonard’s famously erotic 1767 painting of a girl (the kinetically alluring Stephanie Michels) on a swing being ogled by an aristocrat as she’s propelled skyward by a servant. This vignette develops into a sunnily salacious outdoor ménage à trois, which Stroman with wicked wit sets to the great jazz violinist Stephane Grappelli’s recording of Rodgers and Hart’s “My Heart Stood Still.” The second piece, “Did You Move?” jumps to 1950s New York, where a macho mafioso type torments his cowed, subservient wife as they have dinner in an Italian restaurant. Each time the mob guy leaves the table to go to the buffet, the wife breaks out into fantasies of being a great ballerina, leaping and whirling through the restaurant into the arms of the headwaiter, who becomes her dream Nureyev as the soundtrack soars with the music of Tchaikovsky, Bizet and Grieg. Karen Ziemba is marvelous as the wife, cutting arcs through her dream space like an angel.

The third and longest piece, called “Contact,” presents a prize-winning ’90s advertising guy who hates his success as a huckster to the point of attempted suicide. He finds himself in an underground swing-dance club where couples gyrate in blazing jitterbugs à deux. Enter a mysterious Girl in a Yellow Dress, a stunning siren who plucks any man she wants, explodes into transcendent dance, then calmly moves off. The adman yearns mightily, but he can’t dance. Meanwhile the club vibrates with pop anthems ranging from Dean Martin to the Beach Boys to the climactic “Sing Sing Sing” played by Benny Goodman, like a swing version of Stravinsky’s “Rite of Spring.” Boyd Gaines is superb as the desperate adman, forcing his ineloquent body into simulations of Dionysiac movement. Deborah Yates, with her blond hair and yellow dress, looks like a sun maiden launching into extravagant orbits with her infinite legs. “Contact” has a kind of gallant panache, as if it’s trying to restore the primacy of the American musical through pure dance energy. Stroman has inherited the mantle of the departed dance giants Bob Fosse and Michael Bennett. But her sensibility is different. She calls “Contact” a “dance play” rather than a musical. “I feel like I’m a writer of dance,” she says. “I feel my role in theater is to move the story forward, make the character stronger. Every step in ‘Music Man’ and ‘Contact’ has some motivation, some image or vision, some reason that they’re dancing.” The last piece in “Contact” was born when Stroman visited a New York afterhours dance club. “Out of the crowd came this girl in a yellow dress. She’d step forward, choose someone to dance with and then she’d disappear. I became obsessed watching her. I thought, ‘This girl is going to change someone’s life—tonight’.”

Stroman sees dancers the way poets see words. “Ever since I was a little girl I would imagine music, and I’d see hordes of people dancing in my head and I’d imagine these huge scenarios.” Her childhood in Wilmington, Dela., had a musical accompaniment. “My father played the piano. He’s 85, he still does. He played old standards, Kern, Gershwin, Rodgers, the music from the people who made Broadway. I’d watch Fred Astaire and Ginger Rogers movies and I understood how music supported the dance, how their dances were dramatic situations. Music makes my brain dance.”

Stroman served her stint as a dancer. At an audition for a revival of Vincent Youmans’s “Hit the Deck” she was the only one picked out of 300 dancers. But choreography was her passion. In 1987 she choreographed a revival of “Flora, the Red Menace” at a tiny Greenwich Village theater. Director Harold Prince saw it and hired her to choreograph his New York City Opera production of “Don Giovanni” and eventually his hit 1994 revival of “Show Boat.” By then she had already become a major figure with “Crazy for You,” in which she placed dancers on the tops of limousines, on corrugated-iron roofs, wielding miners’ pickaxes. “Steel Pier” and “Big” were unsuccessful shows, through no fault of her continually inventive choreography. For Trevor Nunn’s production of “Oklahoma!” at London’s Royal National Theatre, she had the guts to replace Agnes de Mille’s legendary choreography, the first time that had been done since the show opened in 1943. The results earned critical praise.

Stroman has opened new horizons for Broadway’s talent pool of dedicated dancers. “I’ll give a dancer a combination, then make them do it with different emotional ideas. ‘Now do that combination flirtatiously. Now do it aggressively. Do it as if you had six Margaritas’.” For “Music Man” she even made them musicians. “I brought in a trombone teacher. At the curtain call, the entire company will play “76 Trombones.” Right now the embattled American musical is uncertain in its voice. But Stroman is making it dance like a dream.