SHE played a swinger on “Ally McBeal” – but from now on, they’ll call her “the girl in the sling.”

As Carla, the saucy sex kitten of Broadway’s “Nine,” Jane Krakowski makes an entrance – and an exit – that literally stops the show.

Clad in a towel and suspended by a silky white sheet, she drifts 40 feet down from the ceiling like a fallen angel, taunting a smitten Antonio Banderas.

Mission accomplished, she flies back up again – upside down and singing away.

Ally who? After “Nine” opens tomorrow, it’ll be all about Jane – and her no-strings-attached show-stopper.

“I didn’t want to look like a puppet,” Krakowski told The Post, explaining why she learned to “fly” the circus way, using gravity, a sheet – and no harness.

“She’s very brave,” says “Nine” director David Leveaux. “She’s a joy to direct because she’s just totally open to every possibility.”

Krakowski, 35, was certainly open to trying her hand at TV, playing Elaine, the airhead sexpot on “Ally McBeal.”

But her roots are pure Broadway. You may have caught her in “Starlight Express,” whizzing by on roller skates, or belting out “I Want to Go to Hollywood” in “Grand Hotel.”

And while she says she loved life on the small screen, she’ll think twice before playing another Elaine, with her tacky clothes and nonstop mouth.

“Because ‘Ally’ was on TV so long, people didn’t realize I was not that person,” Krakowski says.

And not only does TV make you look heavier, says the wafer-thin actress, “but the other girls were even more extremely thin than me. We used to say there was something in the water!”

So she’s more than content to be back on stage in “Nine,” a revival of the 1982 musical based on Fellini’s “81/2,” about a director with writer’s block and women problems.

“There’s nothing Antonio Banderas can’t do,” she declares. “He’s a perfectionist . . . He came in the first day of rehearsal with the entire score known and ready to go.”

Working with him, she giggles, is “delicious.”

On Valentine’s Day, the cast arrived for rehearsal to find 18 bouquets of roses – one for each woman in the cast – all of them from Banderas, the only man in the show.

“Now that was really classy,” Krakowski says.

“The nature of the show is that Guido Contini is in love with every one of us, and Antonio makes each of us feel like that every night.”

Her boyfriend, lyricist Charles Hart, may not have been jealous – but Melanie Griffith, Banderas’ wife, has been spending so much time backstage that “we adopted her,” says Krakowski.

“Melanie is a very lucky woman, and she knows it,” she says.

“I think she was a little nervous knowing her husband was going to be doing a show with all these women, but Antonio’s just a great man and a great husband – and when she met us, she realized it’s not really about that.”

Maybe not, but then there’s the little matter of The Dress.

Little it is – a skimpy, nude mesh bodysuit dripping with crystals that Carla wears when she isn’t wrapped in a towel.

“Our brilliant costume designer, Vicki Mortimer, came up with it,” Krakowski says, lifting the minuscule dress from the plastic bin where it rests between shows.

“She saw a crazy photo of a woman being splashed with water and said, ‘I’m going to make that into a dress!’ “

The first time Krakowski tried it on, she says, it was so revealing, she wanted to cover herself. Then Leveaux walked in “and he made pleasing comments.”

Like?

“Actually, it was the lack of comment – the dropped mouth with a slight grin,” she says.

“And I knew it was the right dress!”