Within the first few minutes of the sibling dramedy “The Skeleton Twins,” there’s a phone call from a hospital informing a woman (Kristen Wiig) that her brother (Bill Hader) has just tried to slit his wrists. The news is so upsetting to her that it derails her own plans to swallow a handful of sleeping pills.

That’s your first sign that this isn’t just another skit by the “Saturday Night Live” veterans. Though there are moments of silliness that remind you of the goofy, quicksilver brilliance of these former sketch-comedy whiz kids, the movie is a serious and surprisingly affecting meditation on family and the legacy of self- destruction.

Why have Milo (Hader) and Maggie (Wiig) tried to kill themselves on this same night, a continent apart? (He’s in Los Angeles, she’s in Nyack, N.Y.) It isn’t just because their father did himself in when they were young. They also share a kind of cosmic connection that only close siblings can.

“The Skeleton Twins” — which takes its title from a pair of his-and-hers Day of the Dead toys that Milo and Maggie played with when they were kids — is a poetic evocation of a shared morbidity that spans time and space. Not just a morbidity, but an instinct to save each other, even when — maybe especially when — the other’s darkest secrets have made him or her unreachable.

That bond is illuminated on screen by the real-life friendship of the lead actors, who bring an at-times frighteningly believable brother-sister dynamic to the sharply told tale (written by Mark Heyman and director Craig Johnson). Their relationship veers from painfully awkward tension to moments of giddily intense emotional intimacy.

Siblings Milo (Bill Hader) and Maggie (Kristen Wiig) reunite for the first time in a decade after Milo’s suicide attempt in “The Skeleton Twins.” (Roadside Attractions)

When the film opens, Milo, a gay failed actor, and Maggie, a married dental hygienist, haven’t spoken in 10 years. After Milo gets out of the hospital, Maggie’s invitation to her brother to temporarily move in with her and her husband, Lance (Luke Wilson), an amiable doofus who calls people “amigo,” seems at first like a terrible idea. Milo is a caustically funny club-crawling negaholic, while Maggie and Lance lead quiet suburban lives of streaming Netflix comedies and commuting.

At the same time, there are moments when their differences melt away, as when Milo leads Maggie in a delightfully silly duet of lip-syncing to Starship’s cheese-tastic 1987 power ballad “ Nothing’s Gonna Stop Us Now.”

But the movie is more than a showcase for Wiig and Hader’s chemistry. Over the course of the tale, metaphorical skeletons, in the form of old relationships, come dancing out of both Maggie and Milo’s closets. Though these ghosts partly explain — and partly deepen the mystery of — the characters’ self-destructive impulses, they are essentially distractions. The central focus of the film remains Milo and Maggie’s journey, even when the wakes of other, more heavily freighted vessels swerve dangerously across their path, threatening to capsize the siblings’ little lifeboat.

“The Skeleton Twins” is a small, closely observed chamber piece. That doesn’t mean it’s trivial. It’s an ample vessel for Wiig and Hader’s talents and tastes, which tend more toward the odd but telling detail than to outsize farce.

The actors have an obvious rapport. It’s deep enough to evoke the ties, entanglements and bloodletting of a real kinship. But Wiig and Hader’s instincts as entertainers are keen enough to know when to stop cutting.

The humor and the poignancy of “The Skeleton Twins” come not from what Maggie and Milo have suffered — or inflicted on each other — but what they have together survived.

★ ★ ★ ½

R. At area theaters. Contains obscenity, sex, drug use, sexual dialogue and mature thematic material. 92 minutes.