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Screwball comedy was already a retro affair when Peter Bogdanovich mastered it in 1972 with “What’s Up, Doc?”

Four decades later, that ageless throwback is the standard to which the director aspires in “She’s Funny That Way,” an enthusiastic but low-fizz romantic farce that gets by principally on the charms of a cast speckled with gifted funnymen (and, more particularly, funnywomen).

At once invoking genre forebears like Ernst Lubitsch and contemporaries like Woody Allen, this busy tale of a Brooklyn call girl wreaking havoc among the romantically frustrated cast and crew of a dud Broadway play accumulates the necessary narrative chaos without ever building a full head of comic steam. The diverting result will find a modest audience principally among those old enough to recall Bogdanovich’s glory days.

“She’s Funny That Way” was initially, and more intriguingly, titled “Squirrels to the Nuts,” a reference to an irresistible nugget of do-your-own-thing philosophy from “Cluny Brown,” Lubitsch’s last completed film: “Some people like to feed nuts to the squirrels, but if someone wants to feed squirrels to the nuts, who am I to say nuts to the squirrels?”

It’s a line that is also quoted ad nauseam in Bogdanovich and ex-wife Louise Stratten’s script, conceived in the 1990s as a vehicle for Stratten and the late John Ritter. Here, the line serves as the go-to come-on used by lecherous theater director Arnold (Owen Wilson) to lure pretty, impressionable young things into bed. Escort and aspiring actress Izzy (Imogen Poots) is the latest in a long line of these, bowled over when Arnold offers her $30,000 to quit her night job and pursue her dreams.

That, too, appears to be standard practice for Arnold, who somehow has a vast concealable income more akin to that of a Hollywood mogul than a director of creaky plays such as “A Grecian Evening.” A turgid-looking romantic drama, the play teams Arnold with his actress wife Delta (Kathryn Hahn), her celebrity co-star and ex-lover Seth (Rhys Ifans), and nebbishy playwright Joshua (Will Forte), who is smitten by Izzy the second she — to Arnold’s surprise and considerable dismay — walks into the audition room.

This conflict-rife quintet scenario already has rich potential for raucous bed-hopping, but Bogdanovich and Stratten are far from done: There’s also Joshua’s embittered psychologist girlfriend Jane (Jennifer Aniston), her neurotic elderly patient (and obsessed former client of Izzy’s) Pendergast (Austin Pendleton), Joshua’s disguise-loving private-eye dad (George Morfogen), and so on and so forth.

This kind of amorous carousel structure is a favorite of Bogdanovich’s, who has employed it to variable effect across his filmography: “She’s Funny That Way” never swirls with the wistful elegance of 1981’s “They All Laughed” (whose star, Audrey Hepburn, is lovingly referenced in, as well as by, Poots’ character), but it certainly has more snap and charm than, say, 1988’s long-forgotten “Illegally Yours.”

What it’s missing, however, is any playful sense of truth: Hollywood’s greatest screwball comedies, even at their daffiest, hum with pointed, perceptive sexual politics. Here, the bumper-car series of romantic collisions is entertaining enough, but viewers aren’t invited to root for any two characters’ union or separation: No relationship in the film is especially distinct from another.

When Aniston’s character complains of her meek other half that playwrights “write plays, they don’t think about life,” it’s hard not to level an equivalent accusation against Bogdanovich and Stratten’s screenplay.

This lack of depth even by the standards of a flighty genre would matter less if the film were more consistently hilarious. For every comic zinger or setpiece that lands just right, there’s at least one other that falls ever so slightly behind the beat: It’s telling, moreover, that the film’s defining one-liner had to be lifted from another movie.

It’s perhaps easier to blame any rhythmic deficiencies on Bogdanovich’s forgivable rustiness — this is, after all, the first theatrical feature he has directed since 2001’s “The Cat’s Meow” — than the high-energy efforts of the cast, most of whom are doing their best by the material.

Aniston and the ever-reliable Hahn may be the chief laugh-getters among the principals, though no ensemble member hits her marks with more riotous precision than British comedienne Lucy Punch, a scream in an all-too-brief bit part.

Unfortunately it’s fellow U.K. import Poots, as the film’s ostensible protagonist, who seems somewhat overwhelmed by her co-stars, mugging a little too hard with a mayonnaise-thick Brooklyn accent that never quite convinces. An entirely extraneous framing device that sees her narrating the events years later to Illeana Douglas’ cynical showbiz journalist doesn’t allow her to come any more into focus.

In its best moments, “She’s Funny That Way” defies its careless construction to allow Bogdanovich’s sharper instincts fleetingly through; here’s hoping it’s not another 14 years before he gets back on the merry-go-round.

MPAA rating: R (for some language including sexual references)

Running time: 1:33

Opens: Friday at the Gene Siskel Film Center, 164 N. State St., siskelfilmcenter.org