HBO is no stranger to true crime, though its offerings tend to be more prestige than your average, with documentaries such as the unrelenting sex cult nightmare The Vow and The Yogurt Shop Murders, a measured reinvestigation into the deaths of four teenage girls in Texas in the 90s. They have form, too, in drily funny sagas, such as McMillions, about a high-stakes conspiracy to fix the McDonald’s Monopoly promotion. Rarely are their documentaries both solemn and bizarro, with the exception perhaps of The Jinx. An unnerving tale of millionaire real estate heir turned convicted murderer Robert Durst, it occasionally lingered on the stranger points of his story, like the time he shoplifted a $6 sandwich for kicks.

All this makes sense, really: it’s not like most homicides lend themselves to a deadpan retelling. A Killer Story is not laugh-out-loud funny, either. But this very meta three-parter manages to tell not one but two killer stories, one disturbing and the other absurd. The first concerns a woman, Dana Chandler, who is sentenced to life in prison for the murder of her ex-husband and his new girlfriend. The second is about a true crime-obsessed stranger, Eileen Umbehr, who becomes fixated on the case, spamming a journalist with tips. The emails from Umbehr were, says Joe Sexton – previously of the New York Times and investigative newsroom ProPublica – “a crazy assortment of shit … I [didn’t] know whether to call the cops on her or fucking hire her!”

Sexton – an editor on multiple Pulitzer-winning projects – swears a lot, and his account of the email campaign from “pyjama lady in Kansas” overflows with profanity. Her 2,714th email changes his mind, however; Chandler has had her state conviction overturned, writes Umbehr. It was time for Sexton go to Kansas, to meet the couple he describes – with more than a hint of fatigue – as “the most earnest fucking people you [could] ever meet in your life”.

We flash back to 2002, when Karen Harkness and Mike Sisco were found dead in their home. The couple had visited a casino that night, but there was no indication that this was a burglary gone wrong, with money and jewellery left untouched. Rather, says Ray Lundin, formerly of the Kansas Bureau of Investigation, “whoever did the killing was motivated by emotion” – in other words, somebody known to the couple. Chandler becomes the main suspect, but there isn’t enough evidence in the view of the district attorney to press charges. That is until a TV crime special about her airs on CBS, and a new prosecutor decides to proceed with a legal case. Her eventual arrest was also caught on television cameras.

This is a story about a very public murder case, then, but it’s also about Umbehr and her husband, Keen, a former waste collector who moonlighted as a local newspaper columnist and later qualified as a lawyer (at one point, hysterically, Sexton refers to him as “fuckin’ Bob Woodward”). The Umbehrs’ preoccupation with the case is clear, with Chandler not only dominating conversation at home but also becoming the subject of their prayers. They don’t only believe that she is innocent, however – they also believe they know who killed Harkness and Sisco. Roll credits!

This could, of course, be a regular documentary about a miscarriage of justice but of course it’s not. In episode two we meet the person the Umbehrs are convinced is the real killer – but is their apparent evidence enough to justify involving every single law enforcement body in Kansas? Do the Umbehrs worry, asks Sexton, that they’re doing to this new “person of interest”, as they call him, exactly what was done to Chandler?

There are some serious flaws in that initial case put forward against Chandler. But A Killer Story isn’t about that, ultimately. Rather, it’s about the pull of true crime, and the power of armchair detectives – not just posting on Reddit, but reaching into a real-life murder case and deciding that they know what’s best for the accused. “Certainty is a dangerous notion,” says Sexton, who had expected to blow the case wide open, but instead ends up entangled in something far messier. A Killer Story is a sideways proposition, but it is rather compelling – a rare true crime story that’s as much about the viewers as it is the victims.

• A Killer Story is on HBO Max now