Over and over again in this haunting film based on the life of yet another Wisconsin serial killer, Jeffrey Dahmer (Jeremy Renner), with a look of fascination on his face, places his ear against the rib cage of the young man he‘s just murdered, straining to hear . . . something. But what, exactly? The heart’s fading beat or the sound the soul makes as it departs the body?

Writer-director David Jacobson doesn‘t know the answer any more than we do, but he’s drawn to the intimacy of such scenes, which, by all accounts, were the only times Jeffrey was able to relax around another person and be, heaven help us, himself. Jacobson must be a bit mad as well to take on such a reviled figure, but he‘s canny about it, re-configuring Dahmer’s real-life time line to catch him in what might be termed his middle period, before the unimaginable (and unfilmable) formaldehyde vats and refrigerated body parts. Here, there are two corpses in the bedroom of Jeffrey‘s otherwise pristine Milwaukee apartment, while in the living room there’s Rodney (Artel Kayaru, in a virtuoso performance), the lithe, love-starved young African-American man Dahmer has picked up in a sporting-goods store, who won‘t sit still and won’t stop talking, despite the sleeping pills Dahmer has slipped into his whiskey and Coke.

Zoning out on the chatter, Jeffrey in his mind travels back in time to his teenage years and impromptu first murder, then to a Sunday morning before church when his father, played with exquisite restraint by Bruce Davison, demanded to see what was stored in the old wooden box in the back of Jeffrey‘s closet. As Lionel Dahmer’s heartbreaking memoir, A Father‘s Story, makes clear, it would be years before he learned what his son was preserving in there, but Jacobson has turned that Sunday-morning encounter into a weirdly suspenseful — and beautifully acted — scene. Watching it raises conflicting feelings, for we pretty much know the nature of the box’s contents (something gruesome), and while we yearn for Dad to discover the truth — and thereby save all of Jeffrey‘s future victims — there’s also a deeply ingrained movie instinct that kicks in at the same time, the one that desires the bad guy to get away with it, if only for a while longer.

Back within Apartment 213‘s red- and orange-painted walls, Jeffrey is in control, relaxing in his armchair, guzzling whiskey and chain-smoking with all the imperiousness of a boulevard queen. He’s unflappable on the surface, but Renner, who is extraordinary, holds in his eyes everything the director‘s flashbacks have shown us about Jeffrey’s career track, from the novice who wept wrenchingly after his first kill, to the sadist who calmly drilled a hole in the head of the young man (Dion Basco) lying in the bedroom five paces away.

The drill, the saw, the acid — Jacobson doesn‘t linger over them, which makes it all the more devastating when, near film’s end, he re-creates an act of bodily transgression on Dahmer‘s part that is shocking and yet so dreamlike that it may not hit you until the drive home. More disturbing is that the moment feels apt, as if such depravity were part of a natural progression of events — which makes this the purest of horror films. Its subtitle is “The Mind Is a Place of Its Own,” and in such a realm, transgression isn’t a step the transgressor pauses over, but one composed of inevitability, forward motion, and a complete absence of doubt and regret.

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