If you follow Broadway news, you likely know that a starry revival of “An Enemy of the People” is set to open there next week. More casual fans, though, may not be aware of an homage to its author, Henrik Ibsen, now unfolding across Central Park, in the form of a new play that’s decidedly giddier in spirit.

The characters and foibles informing “Ibsen’s Ghost: An Irresponsible Biographical Fantasy” nod cheekily to numerous works by the great Norwegian playwright, among them such frequently produced classics as “A Doll’s House” and “Hedda Gabler.” Yet you needn’t be an authority to enjoy this delectably witty, often naughty romp, written by and starring a longtime theater and cabaret favorite, Charles Busch.

Mr. Busch, who’s also a seminal drag artist, appears not as the dramatist but as his widow, Suzannah, about whom many biographical details are retained — albeit with satirical embellishment. The real Suzannah’s stepmother, Magdalene Thoresen (née Kragh), was also a writer, as well as a muse to others (Ibsen among them, supposedly), and Suzannah herself translated a play by the German author Gustav Freytag before settling into domestic life with Ibsen and their son, Sigurd, who became a prime minister, as is also acknowledged here.

In “Ibsen’s Ghost,” Magdalene is played by the indomitable Judy Kaye, one of several comically facile veterans enlisted by Mr. Busch and director Carl Andress. Whirling onstage in one of Gregory Gale’s fancifully elegant period costumes, she apologizes to her stepdaughter for having not stopped by since Henrik’s funeral.

“And my blundering rudeness in criticizing your appearance as the coffin was being lowered into the ground,” Magdalene adds. “But, Suzannah, my darling, that wrinkled polka dot veil.” Suzannah responds: “I wasn’t wearing a veil.”

We then meet Hanna Solberg, a protégée and, as she describes it, platonic mistress of Ibsen who is intent on publishing her diary. Played by a hilariously intimidating Jennifer Van Dyck, Hanna turns up at one point in men’s hunting gear, complete with an archer’s bow and arrows — “I’m a proponent of violent exercise,” she explains — and she declares herself, to an appalled Suzannah, the true inspiration for Nora, the heroine of “Doll’s House,” providing exhaustive detail.

As recreated by Mr. Busch, Suzannah actually invites more comparisons to the protagonist of “Gabler.” Hanna notes her nemesis’s “irrational fear of scandal,” and the playwright and star of “Ibsen’s Ghost” has crafted his role to echo developments and even lines that refer directly to the former play; letters are burned in one sequence, for instance, and a gun is produced in another.

That’s not to say Suzannah is strictly a parody of Hedda Tesman. The winking intrigue that fills this comedy requires individual actors to draw on different characters and plots from Ibsen’s repertoire, as Mr. Busch also playfully acknowledges the ways in which artists use the various people in their lives — and not just for inspiration. 

Mr. Andress keeps the action brisk and ensures the shenanigans don’t, for the most part, tip over into mugging. His fine company also includes a pert Jen Cody as Suzannah’s physically impaired maid, who we learn is also serving Sigurd in quite a different capacity, and Thomas Gibson, cast as a sailor who reveals himself to be Henrik’s son from an earlier relationship, yet has little trouble seducing Suzannah.

“Ibsen’s Ghost” ends happily, with these characters having overcome their differences — if a bit grudgingly, in Suzannah’s case. Asked if she’ll recognize Hanna as “the one and only Nora,” she replies, “Yes. Yes. Call her Nora, Hedda, Beowulf. Be done with it!” If only all creative conflicts could be so crisply resolved.