The dead may not die, but Jim Jarmusch’s movie about them slowly expires. This late-in-the-game spoof of zombie flicks is so resolutely deadpan that eventually it comes to feel like one of the walking dead itself.

The cause of the outbreak of revived corpses in little Centerville is suggested by news reports delivered by TV anchorwoman Posie Juarez (Rosie Perez) about “polar fracking,” which has thrown the planet off its axis. The result, it quickly becomes apparent, is a change in the earth’s day-and-night rhythm, which somehow leads to a zombie apocalypse.

In this case, despite occasional news flashes that similar events are occurring elsewhere (complete with governmental assurances that the fracking is not responsible, part of the script’s feeble satirical edge), the event is kept to the small scale of Centerville and its residents. They’re an oddball bunch, headed by the three-person police force: over-the-hill Chief Cliff Robertson (Bill Murray), ultra-serious Deputy Ronnie Peterson (Adam Driver) and, for diversity’s sake, rookie Deputy Mindy Morrison (Chloë Sevigny). After a run-in with local hermit Bob (Tom Waits) over some disappeared farm animals, they’ll confront the first evidence of the undead infestation at the local diner, where the initial two zombies (Iggy Pop and Sara Driver) have disemboweled night workers Fern (Eszter Balint) and Lily (Rosal Colon) before walking off with what they most crave based on their past lives—in this case, coffee. The cops are also keeping the corpse of Mallory O’Brien (Carol Kane), the town drunk, in a cell awaiting transport, and Ronnie’s surmise that the diner incident involves zombies is confirmed when the elderly wino awakens pleading for Chardonnay.

Soon other citizens will be faced with the necessity of warding off hordes of the undead. They include Miller (Steve Buscemi), a curmudgeonly farmer with a racist streak; Hank Thompson (Danny Glover), the hardware store owner; Bobby Wiggins (Caleb Landry Jones), who runs the gas station where he also sells pop culture stuff, mostly about horror movies; Danny Perkins (Larry Fessenden), who runs the motel; and three inmates at the local juvenile detention center—Geronimo (Jahi Winston), Olivia (Taliyah Whitaker) and Stella (Maya Delmont).

A few other people figure in the ensuing mayhem. One is Dean (RZA), a deliveryman tight with Bobby. Then there’s a trio of “hipster” travelers—Zoë (Selena Gomez), Jack (Austin Butler) and Zach (Luke Sabbat), who check into the motel. And finally, the new undertaker in town, Zelda Winston (Tilda Swinton), who turns out to be a real outsider, and somebody who can wield a snappy samurai sword, which she employs to behead the undead, who promptly re-expire in a puff of special effect smoke. Others achieve a similar effect by shooting the zombies in the head, as expert Bobby recommends.

This is obviously a crowded ensemble, but Jarmusch finds only sporadic ways of using them to good advantage. Most of the picture simply plods along at the ponderous pace zombies traditionally take, with great dollops of quirkiness dropped into the mix for the actors to clutch at like under-inflated life preservers. As usual, Jarmusch doesn’t bother directing them much, leaving each to his own devices, which vary considerably. Some get by; others simply drift. There are occasional moments when the picture breaks the fourth wall, as it were—having Ronnie inform Cliff, for example, that the song by Sturgill Simpson is so familiar because it’s the movie’s title tune, or that he knows that “things are going to end badly” (his mantra) because Jarmusch allowed him to read the script; these quips supposed to feel audacious but just come across as juvenile.

The physical production, of course, is cheesy—that’s pretty much a traditional part of the Jarmusch “charm”—but one would be remiss to overlook the deliberate klutziness of the big special effect that’s thrown into the final sequence, something that explains, as much as anything could, the weirdness of Winston, who’s a very peculiar character even for Swinton, an actress who has exulted in them.

You really have to wonder what drew Jarmusch, whose last film “Paterson” (also with Driver) was one of his best, to an idea that—given the number of zombie comedies in recent years—has already been done, so to speak, to death. In any event, his peculiar brand of whimsy does not breathe fresh life into a genre that would probably be best left buried.