The true-crime tale has lately dominated scripted TV, with miniseries-length dissections of infamous incidents coming thick on the ground. Many of these shows have played as flat reenactments that don’t earn the running time they demand, serials that seem to be more interested in checking items off a list to get us to an opinion about “what really happened” than in finding something transformative in a familiar story. So it comes as a surprise that HBO Max’s “The Staircase” does exactly what its title implies, taking the audience beyond the first level and reaching for a second, elevated story.

This show dramatizes the events covered in the French documentary series of the same title — made in 2004 by director Jean-Xavier de Lestrade and available on Netflix. Both projects are about the death of Durham, N.C., woman Kathleen Peterson, possibly at the hands of her husband, Michael. Here, the two are played by Colin Firth, under suspicion in the show’s present, and by Toni Collette, shown in flashbacks blithely unaware of her impending fate. But the process of literally making “The Staircase” — and the appearance of de Lestrade himself as a character (played by Vincent Vermignon) — enters into the story, adding both intrigue and insight about how crime and its consequences play out in public.

The Petersons’ saga, familiar to those who’ve watched de Lestrade’s work, seems at once to be made for the screen and to defy the sort of simplicity that is most telegenic: It’s no wonder that de Lestrade had to make many episodes rather than a documentary feature. Kathleen died after falling or appearing to fall down the staircase of the family home; a death of this kind had happened in Michael Peterson’s inner circle previously. Compounding the suspicion swirling around the halting, awkward Michael was not merely his secretive mien but the fact of his actual hidden life as an avowed bisexual, closeted to his wife.

As Michael, Firth is excellent: Scenes depicting the character’s halting attempts to cruise other men perfectly leverage Firth’s ability, displayed in “The King’s Speech” and “The English Patient,” to undercut his looks with painful insecurity. (These scenes, too, are a welcome use of show creator and director Antonio Campos’ skills: He directed Rebecca Hall to great effect in the 2016 film “Christine,” another project about a person feeling the pain and rage of living a life estranged from herself.) And he’s surrounded by able performers, including Collette, who makes you feel Kathleen’s eventual absence by living as loudly as possible, Dane DeHaan as the black sheep among the family’s children, and Michael Stuhlbarg as a defense attorney confronting a bad set of facts and an unsympathetic client.

But all of these ingredients might have added up to a rote retelling of a story already available in documentary form were it not for the de Lestrade character. A telling of Michael Peterson’s story would, necessarily, include the role the documentary played in his becoming notorious, but the presence of this plotline still feels revelatory for the mere fact of this series’ pulling back the curtain. It reveals a process of narrative-building that’s not unethical but is endlessly consuming, grinding up Peterson family tragedy for copy. We first meet de Lestrade as he shuffles through U.S. newspapers with his producing partner Denis Poncet (Frank Feys), looking for the tale that will keep audiences on the hook. He’s finally convinced when Poncet tells him, in subtitled French, “Innocent? Guilty? The Peterson ending will always be tragic.”

Documentary filmmakers have different incentives and imperatives from journalists; de Lestrade never pretends to himself that he’s going to tell the Peterson story straight, and we see him fight in the editing room to generate suspense, even if artificial. In the center of his frame is Michael, so consumed with the emotions of loss — and, possibly, guilt — that he’s unaware of just how much further his life may yet change.

That’s a key element of this fascinating drama: the ability of people to metabolize change under massive pressure. The children in the Peterson family — some of them adopted after their own mother died in a manner similar to the way Kathleen would — absorb the events happening to them as just another indignity in a life that hasn’t been short on loss. And Michael’s reactions are in keeping with the person we’ve met and spent time with: He’s squirrelly, inward, a mystery even to himself.

Which expresses itself through de Lestrade’s lens; cleverly, “The Staircase” toggles at times between showing Michael as those around him see him and showing him as audiences eventually will. One might accuse the show of trying to have it both ways — decrying our media culture of rapacious violence while indulging in it — if both halves weren’t so carefully made and so probingly curious. This series is more concerned with asking questions than with making statements. It follows the evidence where it leads: What’s refreshing is that that evidence is less about guilt or innocence in a case on which the court has ruled, but about the strangeness and unknowability of the human heart.

The first three episodes of “The Staircase” premiere on HBO Max on Thursday, May 5, with new episodes dropping each week after that.