It’s hard, at first, to see what drew Renée Zellweger to the lead role of “The Thing About Pam.”

Zellweger, in an attempt to resemble the real-life convicted murderer Pam Hupp, forces herself to act through a shroud of body prosthetics. The show’s writers have stripped away subtext, dimming Zellweger’s sparky comic timing. It’s only in the series’ third episode that a tie to Zellweger’s past work becomes clear: Rising to take the stand as a witness in a murder trial, Pam sees her name in lights. In the criminal-justice system, she’s found her own kind of stardom.

“Chicago” this isn’t — that movie allowed Zellweger to be as shrewd and sharp as her character was callous and oblivious. But “Pam,” a limited series based on Hupp’s true story, has this much in common with Zellweger’s famous musical role: It attempts to make points about the hungers and the vanities that drive people to kill. Pam, the show contends, found as a central figure in a 2011 murder case a way to matter; a prosecutor obsessed with finding a clear narrative, true or not, was all too willing to exploit her need.

Pam, a Missouri native, provided testimony in the murder trial of Russ Faria (played here by Glenn Fleshler). She had cultivated — obsessively, in this show’s telling — a friendship with Russ’ wife Betsy (Katy Mixon), who was terminally ill; when Betsy was found stabbed repeatedly, Pam provided testimony about Russ’ volatility and substance use, and secured after Russ’ conviction a trust for his daughters. She’s helped along at ever turn by Judy Greer’s Leah Askey, a prosecutor who enlists Pam as an ally. The show makes intriguingly clear that Leah is out of her depth and the beneficiary of an ethos in unthinking favor of getting “bad guys” put away; she’s aided by a judge with whom she has a cozy relationship, and by the presumption of guilt.

Pam has a part to play in getting Leah a win, and allowing the gears of justice to chew up a man who’s not guilty beyond a reasonable doubt but who seems close enough. As Russ’ lawyer, Josh Duhamel is tasked with playing notes of utter incredulity again and again. It’s fascinating to see — on the network that has been airing the fairly prosecution-friendly “Law & Order” suite of dramas for decades — a defense attorney shown as in the right, and indeed the victim of a rigged system. (These are baby steps, but real ones; the next progression might be a positive depiction of an attorney defending a client who isn’t obviously innocent.) But Pam, enough of a mastermind to get what she wants, seems blissfully unaware of the case’s systemic consequences beyond herself. Zellweger gets to play avarice, as Pam really wants that money, but also a sort of delusional neediness. One suspects, at moments, that in ensuring her friend’s husband gets put away for a crime he didn’t commit, she really believes she’s doing what would make Betsy happy.

Not that the show tends to give its performances room to breathe. If it really trusted its star, it might either have cast someone who fulfilled the brief of looking like Pam Hupp or have allowed Zellweger to summon her essential spirit without prosthetics that degrade subject and star both. Pam’s angst came from somewhere, but — as on FX’s “Impeachment” — there seems to be a conflation of physical size and lack of grace with mania, a connection emphasized by how attention-getting the uncanniness and weirdness of Zellweger’s reinvention. (In her prosthetics, she simply doesn’t look or move in a way that feels real. It’s a problem!)

A show that really trusted its star might also have allowed Zellweger to shade her character by parceling out backstory slowly, rather than — in the current vogue — presenting one flashback episode deep in the series run to attempt to explain everything. Meanwhile, Greer’s character is uncomplicatedly awful — which is itself a complicated proposition given her role on the conviction side of things, but which saps a certain tension from her scenes. Once we figure out she’ll always say the most objectionable thing, where is there to go? The same’s true, in the opposite direction, for the likable and heroic Duhamel character.

And Zellweger is, too often, drowned out, whether by the loudness of the production’s reshaping her body or by literal narration. Pam Hupp’s story rose to national infamy in part due to coverage on NBC’s “Dateline,” and this series uses “Dateline” correspondent Keith Morrison to comment on the action. His intrusions into the narrative — larded with folksy metaphor — seem intended at least in part facetiously, as a way to comment on the excesses of the genre that gave us “Pam.”

But the end result is an ebbing-away of Pam’s story in favor of a media metanarrative that’s far less compelling; the show is, in moments, more about the customs and rhythms of “Dateline” than it is about a crime story. The entry of a “Dateline” producer as a character midseason comes as a grim development: The show seems to be positioning NBC’s newsmagazine within this narrative as a truth-telling agent of change. It’s not that “Dateline” didn’t play a role here, but that role seems tangent to larger and more interesting points about human nature and about the American way of justice that “Pam” toys with through its first four episodes. One hopes the show’s conclusion picks them up in a more direct and concerted manner: It’d be a shame if Zellweger’s first acting gig after her Oscar-boosted return to Hollywood were, ultimately, little more than NBC cross-promotion.

“The Thing About Pam” premieres Tuesday, March 8 at 10 p.m. E.T. on NBC.