The killing of Lyra McKee, a journalist shot while observing a riot in the Creggan area of Derry, Northern Ireland, on 18 April 2019, is a case that remains officially unsolved. Last month, three men were found not guilty of her murder after a two-year trial; so far, there has been only one conviction, for possessing the gun that killed her.

That a member of the republican paramilitary group the New IRA fired the weapon is not in question. Many of the approximately 150 people who were standing within metres of him at the time must know who he is. But this is a part of Northern Ireland where police work is still, more than 25 years since the Good Friday agreement, met with violent intimidation or resolute silence. The extinguishing of McKee’s bright, hopeful talent is a story destined not to end in relief or resolution.

The challenge faced by the film-maker James W Newton, in his three-part documentary on the investigation into McKee’s death, is to turn an agonisingly unsatisfactory situation into satisfying journalism. He struggles. The programme is made with care and skill, but it is a bleak situation in which not much can happen and few insightful things can be said.

As the title indicates, The Murder Detective is not chiefly about McKee. Instead, having been granted unprecedented behind-the-scenes access to a terror-related murder investigation by the Police Service of Northern Ireland, it concentrates on Jason Murphy, the detective hunting for the killer. We see raids on the houses of suspected New IRA members and hushed meetings with MI5 agents whose identities are concealed, but Murphy’s work is based almost entirely on one type of evidence: CCTV footage of the crime.

This gives The Murder Detective its startling opening scene. To the sound of increasingly panicked chat on police radios, a line of armoured vehicles is surrounded, then pelted with petrol bombs; a stolen truck is driven up to the junction in front of the police vans and torched. Then a figure in a hoodie, a mask and striped Adidas tracksuit bottoms starts firing a pistol.

As Murphy and his team pore over the pictures frame by frame, they spot a documentary camera operator in the background of one shot, which leads them to the case’s strangest quirk: there is more footage out there. Much more, in fact, because, when the riot began, the TV presenter Reggie Yates was there, making a documentary for MTV about Saoradh, the political wing of the New IRA. Murphy commandeers the tapes.

The Yates film is by far the most remarkable part of The Murder Detective. Yates is in the cars and houses of people Murphy suspects have close links to the New IRA’s leaders, looking over their shoulders as their phones flash up Facebook notifications reporting that the police are in the vicinity and something is about to go down. As he walks through the crackling Derry night with these forceful young men, the sense that Yates has lost control of his project becomes overwhelming. Eventually, after being told by a local person that the riot may be taking place only because he is there, Yates withdraws; he is not present when the shots are fired.

Questionable as Yates’s actions may be, it’s noticeable that the rest of The Murder Detective lacks a scoop to match the MTV documentary (which has not been aired). Newton attempts to give us a backstory for Murphy, but finds nothing unusual to explain what drives him psychologically. The programme can’t decide whether this is Murphy’s show or not; he never emerges as an engaging protagonist. As for the investigation, Murphy and his team arrest and interview people whom they believe to be increasingly senior members of the New IRA. But since all of them refuse to say anything, each interrogation is less compelling than the last.

Having embedded itself with the cops, The Murder Detective seems to feel obliged to give them extensive screen time, an investment the police never repay. More memorable are the scenes with McKee’s grieving family – particularly her raging and focused sister Nichola – but her work as a journalist is only briefly explored. Perhaps it was not considered to be relevant, as it seems McKee wasn’t targeted deliberately – she was standing near the police when they were shot at – but it would have been valuable context, since McKee wrote about how, in a supposedly peaceful post-Troubles Northern Ireland, young men have been left behind, making them vulnerable to becoming the victims or perpetrators of violence.

The Murder Detective mentions that the New IRA hides behind a small army of young male recruits, but it doesn’t analyse the socioeconomic factors that enable it to do so. Instead, it watches the police bang their heads against the same wall, over and over. Justice for McKee remains tragically elusive.