A sharp, sophisticated modern screwball comedy that recalls its forties predecessors without being slavishly imitative, “Mistress America” confirms Noah Baumbach’s status as the new generation’s Woody Allen, a prolific if uneven filmmaker with a distinctive voice and a sharp eye for absurdity who’s also capable of an underlying strain of poignancy. The major difference is that he’s not so prone to the narcissism that has often affected the older man’s work, though as in his earlier film “Frances Ha” he takes the opportunity to spotlight his significant other, Greta Gerwig, who also (as in “Frances”) co-wrote the script.

The initial focus is on Tracy (Lola Kirke), who arrives in New York City as a Barnard College freshman and finds the campus literary scene to which she aspires rather intimidating, though she quickly develops a friendship with another nervous newbie, Tony (Matthew Shear). Her mother (Kathryn Erbe) suggests that she look up Brooke (Gerwig), the daughter of the man scheduled to become her new father-in-law, and though Tracy’s reluctant to contact someone so old (Brooke’s thirty!), she eventually gives her a call. Brooke turns out to be extraordinarily welcoming and arranges a meeting in Times Square.

Brooke is also incredibly effervescent and well-connected, as well as overflowing with entrepreneurial dreams that, unhappily, never seem to progress beyond the planning stage. She’s an aerobics instructor who also claims to do interior decorating, but is especially notable as a fixture at clubs, parties and gallery events, and has in mind writing a superheroine comic book called Mistress America and opening a restaurant that will be the best of everything. She also has a wealthy boyfriend named Stavros, she enthusiastically reports, but he’s off in Greece doing something or other.

Tracy is initially enthralled by Brooke, and happily becomes a hanger-on. Indeed, she’s so taken with her new, endlessly exuberant friend that she begins to conceive of a story based on her that might just win her membership in the snooty Barnard literary society. Of course, she’s oblivious to the fact that she might just be taking advantage of Brooke, who might not appreciate having her life serve as the inspiration for a college kid’s semi-fictionalized paper.

And, of course, Brooke’s ambitious plans—as well as her romantic fantasies—all fall through, leaving her desperate somehow to recoup. Her answer is a trip out to Greenwich, Connecticut, where her old friend and now bitter rival Marie-Claire (Heather Lind), who she claims stole her idea for successful clothing line (as well as her cats), is now living in suburban luxury with Dylan (Michael Chernus), a man whom she also snatched from Brooke. The plan is to coax funds for the restaurant from the old boyfriend and after a fashion Brooke succeeds, though not with the outcome she’d been hoping for. But the episode is drawn in true screwball form, with Brooke being driven to Connecticut by shy Tony, with Tracy and his new, suspicious girlfriend Nicolette (Jasmine Cephas-Jones) in tow, and a slew of other characters—an antagonistic neighbor and a bevy of pregnant women holding a book club session—dragged into Brooke’s sales pitch, during which news of Tracy’s story also leaks out. It’s the sort of elaborate one-entrance-after-another contraption that one often finds in the finales of comic opera.

“Mistress America” is buoyed by Gerwig, whose breezy, scatterbrained turn channels some of Hollywood’s great comediennes of the past—Carole Lombard, for example. But she also brings to Brooke a glimmer of the insecurity that she’s so anxious to hide from the world. Kirke is fine in what is essentially the straight-man role, but the supporting cast is replete with the sort of stellar character performers that Preston Sturges once formed into a repertory company, among whom Shears stands out as the infatuated Tony, a fellow Tracy continues to depend on even after he’s moved on.

On the technical side, the picture’s fine, with mostly workmanlike cinematography by Sam Levy that turns more virtuosic in the tracking shots inside Dylan’s Connecticut mansion and spiffy editing by Jennifer Lane. The production design (Sam Lisenco), art direction (Ashley Fenton), set decoration (Katie Hickman) and costume design (Sarah Mae Burton) all contribute to an unerring sense of personality and place, and Dean Wareham and Britta Phillips contribute an idiosyncratic score that somehow feels just right.

Like Allen’s films and his own up to this point, Baumbach (and Gerwig’s) “Mistress America” will probably draw a small, select viewership. Others who gorge on the assembly line of raunchy Hollywood comedies won’t know how much better they could have it if they just stepped down the megaplex hall.