A few years back, a musical called “The Prom” won the hearts of Broadway audiences with a tale about teenagers overcoming both their own fears and the narrow-mindedness of others. Though no household names were involved, the cast and creative team were packed with theater favorites, led by the director/choreographer Casey Nicholaw, whose many credits include acclaimed hits such as “The Book of Mormon” and “Mean Girls.”

The new production, “How to Dance in Ohio,” carries less of a pedigree overall; its young director, Sammi Cannold, is a rising star who apparently inherited the project from the late legend Hal Prince, but the majority of its principal performers are making their Broadway debuts, as are composer Jacob Yandura and lyricist and librettist Rebekah Greer Melocik. Yet the new musical, which also focuses on young adults staring down challenges, boasts the same infectiously, defiantly positive spirit, and I’m guessing it’s going to prove similarly appealing in these even more troubled times.

If “Ohio” doesn’t offer the kind of polished virtuosity that “Prom” did, that’s part of its charm. Based on Alexandra Shiva’s 2015 documentary film, the new show follows seven autistic teens and twentysomethings as they meet in a support group led by Dr. Emilio Amigo, the therapist featured in the movie — played here by the likable stage veteran Caesar Samayoa — and plan a spring formal. Dr. Amigo’s patients are inspired by and named after the young men and women in the film.

There’s Drew, a math whiz who’s been accepted at the University of Michigan but isn’t sure if he can comfortably leave home, and Mel, a pet store employee whose goal is to be “Head of Reptiles” at work. Best friends Jessica and Caroline are respectively obsessed with dragons and a first boyfriend, while the precocious Marideth — who catches Drew’s eye pretty much immediately — is preoccupied with “facts,” preferring books and informational websites to social interaction.

Some of these quirks may sound like common symptoms of adolescence and early adulthood, and that’s the point: autism can manifest in different forms, and those diagnosed with it encounter many of the same struggles that face all young people. This message is reinforced in the casting, as the performers playing members of Dr. Amigo’s group identify as autistic themselves, and all imbue their characters with the mix of energy, yearning, and self-consciousness particular to their age group.

Amilia Fei’s perky Caroline, Ashley Wool’s sassy Jessica, Imani Russell’s dry Mel, and Madison Kopec’s painfully introverted but plainly thoughtful Marideth all reminded me of kids I’ve met at various points through my own teenage daughter. Some of the passages in “Ohio” that touched me most deeply, in fact, saw the parents of several of these characters—movingly played (and powerfully sung) by Haven Burton, Darlesia Cearcy, and Nick Gaswirth—either savoring their children’s progress or worrying about their future. 

Mr. Yandura’s tender and bouncy melodies offer savvy showcases for the performers, who also include an immensely endearing Liam Pearce, as Drew; Conor Tague as the more carefree Tommy, and Desmond Luis Edwards as the flamboyant Remy, an aspiring social media personality. Ms. Melocik’s book and lyrics can be surprisingly clever and affecting; while a song title like “Terminally Human” may threaten preciousness, the message itself is made with disarming directness.

“Are any of us safe from pain/Whatever precautions we take?” Dr. Amigo asks in the song; he then resolves that his patients are, like himself, “terminally human/Which means we’re alive.” It’s the kind of reassurance we can all use right now, and “How to Dance in Ohio” makes the point as joyful as it is irrefutable.