With a pack of fairy godmothers, a nefarious spindle, and one extremely long nap, "The Sleeping Beauty," which runs through Sunday, is a rather far-fetched tale. Nearly as improbable is New York City Ballet's production of it—one of the most elaborate in the company's repertoire, said its stage manager, Marquerite Mehler.

Sara Mearns as the Lilac Fairy in 'The Sleeping Beauty' Paul Kolnik

In the weeks before opening, Ms. Mehler was tasked with examining the 200 costumes and five trucks' worth of scenery featured in the pageant-like production. It was a necessary labor, she said, since much of it belongs to City Ballet's original 1991 premiere of "The Sleeping Beauty."

"Some of it is wearing its age," she said, "so every time we bring it back, we take a look to see what needs to be refreshed."

The ballet is also elaborate in its staffing. Whereas NYCB employs 10 stagehands for a typical show, Ms. Mehler said "The Sleeping Beauty" requires 48: "Twenty-four carpenters, 18 electricians, and six props men."

Many are charged with moving the ballet's grand set pieces, like its 22-foot ship sailing dreamily across the stage, or its 200 feet of wild bramble, which grows over the castle in the second act. While most contemporary productions employ an automation system so that a stage manager can move set pieces around with a few fingers, "The Sleeping Beauty" is resolutely old-school.

"That's one of the most wonderful things about this show: It's all done by hand," Ms. Mehler said. "The stagehands follow the tempos in the score as much as the dancers. It's part of what makes it so charming."