The distance between Brian De Palma’s Dressed to Kill and its source of inspiration, Alfred Hitchcock’s Psycho, is 20 years. The distance between Dressed to Kill and now is 40 years. Those numbers seem impossible in certain respects: the sensory overload of De Palma’s thriller – with its explicitness and gore and vibrant colors – feels much more modern, as do the performances, which have a naturalistic quality that hadn’t completely asserted itself in 1960. And yet the film is also disconcertingly retrograde, tied to ideas of violent gender dysphoria that haven’t advanced an inch from the psychiatrist who explains Norman Bates’s behavior at the end of Psycho.

There’s no way to talk about Dressed to Kill without spoiling the twist a little – just mentioning Psycho gets us most of the way there – so proceed with that disclaimer in mind. But there’s really been no time in its 40-year history where controversy hasn’t trailed the film: it’s been called a high-toned slasher film, an expression of leering misogyny, and more recently, a prime example of on-screen transphobia. For De Palma fans, it’s the most problematic fave in a career full of them, a provocation both deliberate and accidental, reflecting and challenging the cultural norms at the time. To watch it is to exist in a dual state of attraction and repulsion, which is completely apropos for a film of relentless doubling, centered on characters who are at war with themselves.

From the very first scene, a deliciously pornographic riff on the shower scene in Psycho, De Palma is already setting Dressed to Kill on the razor’s edge between sexual desire and murderous violence. The Janet Leigh of this scenario is Kate Miller (Angie Dickinson), a middle-aged housewife whose husband shaves obliviously as she explores her own body in the bathroom. (The morning sex they have later is a dreary grind over the chatter of a clock radio.) The Norman Bates of this scenario is conjured entirely by her imagination, as if the pleasure she seeks is forbidden and worthy of punishment. The real world will soon turn this dark fantasy into reality.

But not before De Palma unleashes one of the great set pieces of his career. On an afternoon visit to the Metropolitan Museum of Art, Kate enters into a wordless flirtation with a handsome stranger in dark glasses – and this being a De Palma film (and this being the world), there’s always the threat that such a casual erotic rendezvous could turn dangerous. Kate’s sexual frustration is a primary topic of conversation with her therapist, Dr Elliott (Michael Caine), who has flatly confessed his own attraction to her, but at the museum, she finally seizes the opportunity to scratch the seven-year itch. As Kate and the stranger play a cat-and-mouse game through the galleries, De Palma, a stickler for establishing spatial relationships, turns the museum into a dizzying maze of rooms that connect in multiple directions, which has the effect of amplifying her desire to a fever pitch. A pair of gloves becomes an old-fashioned form of invitation, like an appeal to chivalry, and by the end of the scene, when Pino Donaggio’s score has whipped into a frenzy, one glove is retrieved by the stranger and the other by the person who will eventually kill her.

It turns out there was no reason to fear this stranger – other than the sick joke De Palma makes about Kate discovering he has a venereal disease – but the retribution she feared in the shower manifests itself in the elevator outside his apartment. Time and again in Dressed to Kill, De Palma establishes potential danger and has women rush toward it with heart-stopping speed. Here, we know that a blond killer in a black trenchcoat and a hat is stalking Kate at the seventh floor of an apartment building, and when she discovers she left her wedding ring behind, up she goes to the seventh floor, right into the lion’s den. Her slashing with a razor blade evokes the brutality of Leigh’s death in Psycho, and sends the film reeling into the same uncertainty. We just lost our protagonist. Now what?

With typical brazenness, De Palma outflanks Hitchcock by introducing a second female protagonist, Liz Blake (Nancy Allen), who is also a kind of a mirror image to Kate. Where Kate is a sexually repressed housewife looking to score, Liz is a high-priced escort who’s comfortable leveraging her body to get what she wants – though both woman are, pointedly, subject to the volatility of men. Liz discovers Kate’s body, and partially identifies her assailant through a reflection in an elevator, putting her fate on the edge of the same blade. From there, the film gearshifts into a tense whodunnit where Liz and Kate’s nerdy son (Keith Gordon) turn amateur investigators, convinced that one of Dr Elliott’s patients is responsible for the murder.

There are doubles everywhere in Dressed to Kill: two women, two gloves, two shower scenes, two blondes following Liz around, and, of course, plenty of De Palma’s signature split-screens and split-diopter shots. And there’s no duality that matters more than Dr Elliott and Bobbi – one a clinical therapist who bottles his impulses, the other a “Mother” type in a wig and a dress who springs into action whenever the doctor feels aroused. There’s no getting around the ugly association of gender transition with violence, other than to say that it feels thoroughly aestheticized, of a piece with Psycho and with De Palma’s career-long fascination with split personalities in earlier thrillers like Sisters and Carrie, and later ones like Body Double, Raising Cain and Femme Fatale. His failure to understand a transgender woman as fully human, rather than an exotic and alien phenomenon, is more acutely felt now than in 1980.

Yet the most common charge against Dressed to Kill at the time – and for decades afterwards – is that it’s spoiled by misogyny, due mainly to the gaze-y objectification of its heroines. But that charge seems partly misdirected. Dressed to Kill is about America’s deadly puritanical instincts, levied against women who want to have the type of “lovely afternoon” that Kate seeks out at the Met without repercussions. As horror headed into a decade of slasher movies, which often implied that promiscuous women deserved to be the first ones hacked, De Palma flipped the premise on its head. His women may be marked for death, but they’re framed by a culture where sexuality is a crime.