In the opening minutes of Zarina Shea’s new play, “Let’s Call Her Patty,” we get a detailed sketch of the title character. Patty is a well-preserved Upper West Side resident of a certain age; she’s a “lady of moderate means,” we’re told, which is to say that “anywhere else she’d be super wealthy.” She donates to the ACLU but is miffed when her taxes are raised, and she gets excited when a longtime New York Times columnist, Gail Collins, is scheduled to speak nearby.

Ms. Shea’s protagonist is, in short, either a stereotype or a flat-out parody of a kind of proudly liberal but self-interested urbanite; the hokum-drenched script, which shutters between comedy and pathos without showing grace in either pursuit, makes it unclear whether the playwright is sending up Patty’s milieu or wallowing in it. 

Either way, Patty, who is played gamely but shrilly by a famed character actress, Rhea Perlman, is, to put it bluntly, a dope, and not a terribly sympathetic one — even during the pitiable predicament she soon finds herself in. Railing aimlessly against the establishment, she confuses Mark Zuckerberg with the actor Jesse Eisenberg, who played the tech mogul in a movie. She feeds her dogs onions: Ms. Perlman is called on to chop them throughout the proceedings, loudly, as if the percussion were intended to lend weight to the dialogue. 

Worse still, when it’s disclosed that her friend’s son had to enter drug rehab, Patty assumes it’s the mother’s fault — because, well, the kid went to Harvard, so what else could be the problem? When Patty learns that her own daughter, Cecile, a rising artist in her late 20s, has also developed a substance abuse problem, her initial reaction is complete denial. Cecile is “talented,” her mom protests, and “a smart kid,” and “Jewish.” (At more than one point, Patty shows signs of the supercilious tribalism that antisemites regularly ascribe to Jews, which I guess is supposed to be funny.)  

We don’t really get to know Cecile, who has never quite grown up, thanks in large part to her mother’s coddling. Played by the winsome young actress Arielle Goldman, she’s little more than a specter who emerges periodically to mumble a few words, always seeming sad and lost. There is another prominent character in “Patty,” though, one whose apparent purpose is to both counter Patty’s small-mindedness and encourage empathy for her.

That third party is Sammy, Patty’s niece, whom she and her husband have raised since Sammy lost her mother at the age of 5. (The child’s father is “a very terrible person,” Patty explains.) Although closer in age to the sheltered, childlike Cecile, Sammy seems light years ahead of her cousin in terms of experience and self-sufficiency, and the likable Broadway veteran Leslie Rodriguez Kritzer briefly promises some fresh air in the role.

Alas, Sammy proves to be as cliché-addled and, at times, as ridiculous a figure as her aunt. Her exchanges with Patty are abruptly interrupted by asides in which she rants about Senators Manchin and McConnell and the inevitability that their neighborhood will end up underwater, “because plastic straws are not enough.”

Such outbursts only make legitimate concerns about political corruption and climate change seem inane, almost suggesting that Ms. Shea is satirizing views she presumably supports. Ms. Rodriguez Kritzer and director Margot Bordelon seem to have been stumped by the resulting unsteadiness, and by the canned quality of Sammy’s appeals to the audience and the writing in general.

Ms. Bordelon keeps the pace fairly brisk, to her credit, and “Let’s Call Her Patty” clocks in at a mere 70 minutes in full. In this case, unfortunately, brevity does not prove to be the soul of wit.