A Nordic chill pervades Tomas Alfredson’s adaptation of Jo Nesbø’s typically gloomy Scandinavian crime thriller—one of a series featuring detective Harry Hole—but the frigidity is dramatic as well as atmospheric. Though handsomely produced, impressively shot on location by Dion Beebe and boasting a (mostly) estimable cast, “The Snowman” emerges as something akin to a weirdly turgid “very special” episode of “Criminal Minds”—one that might have been subtitled “Oslo Division.”

Michael Fassbender is Hole, a cynical alcoholic separated from his latest girlfriend Rakel (Charlotte Gainsbourg) and her son Oleg (Michael Yates), who still idolizes him although his mother is now living with another suitor, a doctor named Mathias Lund-Helgeson (Jonas Karlsson). Though protected by boss Gunnar Hagen (Ronan Vibert), he’s anxious for a challenge, and gloms onto a case of a missing woman, Birte Becker (Genevieve O’Reilly), being investigated by his young colleague Katrine Bratt (Rebecca Ferguson). He joins her interrogation of the woman’s husband Filip (James D’Arcy) and the couple’s young daughter Josephine (Jete Laurence).

The disappearance turns out to be connected to a taunting note Hole has received from an anonymous source signed with the figure of a snowman; a newly-constructed snowman is found outside the Beckers’ apartment. The newly-minted team is presently drawn into the case of Sylvia Ottersen (Chloe Sevigny), a woman who is reported missing before she actually is. And all this is played out against the background of a Norwegian attempt to win the Winter Olympics for Oslo being spearheaded by powerful businessman Arve Stop (J.K. Simmons), who some years earlier had taken over the company of a man whose wife had disappeared under similar circumstances. That case, as we see in several flashbacks, was being investigated by a boozy detective named Rafto (Val Kilmer), who—according to his colleague Svensson (Toby Jones), committed suicide. Stop not only has some odd sexual fixations but is also connected to creepy Dr. Vetlesen (David Dencik), with whom Birte had an appointment—but for what purpose?

As if all that weren’t enough, there is another flashback, presented as a prologue, to deal with: a long-ago scene at an isolated house, where a mother (Sofia Helin) and her terrified son (Leonard Heinemann) are brutalized by her sternly demanding lover (Peter Dalle), who is apparently a cop. That sequence ends in a tragedy on a frozen lake when the ice cracks under the weight of a car.

All of these elements are tied together in the end, which brings a certain cyclical symmetry to the tale, but the method of narration is so confused and haphazard that, though the big concluding revelation is both obvious and farfetched, one suspects not only that the three screenwriters struggled to tame the novel’s labyrinthine structure but that Alfredson’s footage has been reworked repeatedly by editors Claire Simpson and Thelma Schoonmaker in an effort to impose some coherence on it. In the end, unhappily, the attempts of these valiant craftspeople prove futile. “The Snowman” remains atmospheric but chaotic, a ponderous, hazy parade of red herrings and misdirection that winds up with a totally implausible, psychologically simplistic denouement that wouldn’t be out of place in a TV crime procedural.

The actors are unable to transcend the formula. Fassbender, showing only a bit more emotion than he did as the android in the recent “Alien” movies, is a sort of black Hole, as it were, and Gainsbourg looks vaguely stricken throughout, even when engaged in sexual contact with him. (She and Yates also have to undergo a humiliating scene toward the close—a cliché that’s staged with a degree of crudeness that seems uncharacteristic for Alfredson.) Ferguson is saddled with a role that is actually quite absurd and also ends with a scene that is, quite honestly, demeaning. Virtually everybody else—Simmons, Karlsson, Dencik, Jones, D’Arcy, and even Vibert, along with Alec Newman as a goofy repairman who shows up at Harry’s pad to deal with an outbreak of mold—serves merely as one in a succession of suspects paraded past the camera to muddy the waters.

There is one joker in the pack, though—Kilmer. Decked out in a ridiculous hairdo and a set of false teeth so huge that it appears that they interfered with his vocal delivery and his dialogue had to be overdubbed later, he swoons and postures to such an extent that his scenes have to be judged as failed comic relief.

One can, however, simply sit back and appreciate Beebe’s chilly widescreen images, shot lovingly in hues of white and gray, and Marco Beltrami’s score, which is surprisingly sophisticated coming from him. Apart from that, one can only hope that this represents an aberration for Alfredson, and that he will regain his touch quickly. As for the possibility of a franchise of Harry Hole films, forget it.