Nowadays, one often hears Jews refer to themselves as “Jew-ish,” accentuating the second syllable in order to proclaim ambivalence about their religious and ethnic identity, suggesting that it is only a close approximation of, or only tangentially related to, actual membership in the tribe. Upon first hearing the title of Monica Piper’s new one-woman play, “Not That Jewish,” one might think, as I did, that the show, which opened on Sunday, is an extended exercise in downplaying, or perhaps even denigrating, Jewishness.

Thankfully, though, as I discovered at last Saturday night’s preview, the title of “Not That Jewish” is ironic; the play, which is directed by Mark Waldrop, is a sensitive and nuanced exploration of a comedian’s life and career in which almost every line, in addition to being hilarious and moving, deals in one way or another with her Jewish identity.

Piper’s 90-minute, intermission-less show, which was commissioned by the Jewish Women’s Theatre in Santa Monica and then ran for 16 months in L.A., begins with her sitting in a synagogue on Rosh HaShanah, under an Eternal Light and stained-glass windows. Piper confesses that she has never had much of a clue what it means to be religiously Jewish. She explains by launching into a description of her upbringing in the Bronx, in a family that was so ambivalent about their religion that, while they did not attend synagogue for the High Holy Days, they put on their best clothes and stood out in front of their apartment building to pretend that they had just been in shul.

The show’s title comes from an episode when the actress was 7; one of her friends told Piper that because her family was not affiliated with a shul, she was “not that Jewish,” a conclusion that was given ammunition from her birth name, May Lee Davis.

From then on, Piper’s life seems to have been dedicated, to a large extent, to proving her friend wrong, by using the Jewish humor that was her birthright in order to create a career in comedy and an outlook on life that, as it turned out, would help her to survive terrible adversity, including two failed marriages and breast cancer.

With an envious talent for mimicry and an extraordinarily expressive face and eyes (making one wonder if the googly-eyed lobster in the show’s logo is somehow related to her), Piper does a marvelous job impersonating the different members of her family, starting with her beloved father, who worked as an entertainer at a resort in the Poconos, and extending to her aunt and uncle who also lived in her building. “Why do they always host us for Shabbat dinner but we never host them?” she asks her mother at one point. The rejoinder: “Would you rather cook for nine hours or take an elevator?”

In addition to appearing both in comedy clubs and on Showtime, Piper has written for “Roseanne,” “Mad About You” and other TV programs; she won an Emmy for her work on “Rugrats.” Her talent as both a stand-up comic and a joke writer is apparent from the fact that she lands line after funny line. When she tries, as a child, to figure out what it means to be Jewish in the absence of shul membership, she is told that it has to do with her mother’s making chopped liver for the holidays. So she concludes that chopped liver is the essence of Jewishness. “So when someone asks you, ‘What am I, chopped liver?’” she tells the audience, “The answer is ‘yes.’”

But as Piper moves to California (adapting the letters on a sign for the Santa Monica Pier to form her stage name) and starts to work in restaurants and comedy clubs, she learns that being glib about her Jewishness can have a cost. Her first marriage, to a tall, blonde, blue-eyed Protestant man, ends not long after the newlyweds attend a screening of Elaine May’s 1972 film, “The Heartbreak Kid,” about a Jewish man who dumps his stereotypically loudmouthed, demanding Jewish wife on their honeymoon in order to take up with a blonde, willowy non-Jewish woman; Piper’s husband insults her by telling her that she is just like the Jewish woman in the movie.

Piper’s second marriage, also to a non-Jewish husband, ends when he turns out to be a cocaine addict. (She does seem to have attracted her fair share of non-Jewish men; a highlight of the show is when she is propositioned in a New York restaurant by Mickey Mantle.) Only after adopting a son, Jake — a decision made after realizing that “if I were an impatient ex-New Yorker, so were my eggs” — and giving him a Jewish upbringing, does she concretize what being Jewish means to her. Her son’s bar mitzvah becomes extraordinarily significant, as does his taking on adult responsibility (and embodying his grandfather’s sense of humor) when it comes to helping her get through her radiation treatments.

Can one Jew be more or less Jewish than another? Piper’s show suggests that these distinctions are unhelpful and even destructive. Rather than denigrating herself for a lack of religious involvement or knowledge of Yiddishkeit, Piper celebrates the aspects of her Jewish identity that are meaningful to her, and that have enabled her not just to find joy in her own life but to bring it to so many millions of other people. In the end, someone who calls herself “not that Jewish” is compellingly and triumphantly so, in ways that should give pause to anyone who tries to define Judaism in a narrowly religious way.

“Not That Jewish” runs at the New World Stages, 340 W. 50th St. Performances are Monday and Thursday at 7 p.m., Friday and Saturday at 8 p.m., with Thursday and Saturday matinees at 2 p.m. and Sunday matinees at 3 p.m. For tickets, $49-$79, call Telecharge at (212) 239-6200 or visit telecharge.com.