Here's a quick question for you: who do you think of when you hear the words "Miss Marple"? If you're my age – fortyish – you'll be picturing Joan Hickson from the BBC; if you're a little younger, perhaps you visualise Geraldine McEwan or Julia McKenzie. But before any of these, Miss Marple was played on the big screen by Margaret Rutherford, in a series of famously unfaithful adaptations which the author Agatha Christie was rumoured to hate. This intriguing and suitably-riddling play brings Christie and Rutherford together, tracking their initial enmity, yet gradually revealing that they have more in common than it seems.

Philip Meeks' script, which made its debut in Edinburgh a few years ago, bears all the hallmarks of a classic mystery. There's a terrible secret buried in the past – a secret which Christie, like her fictional detectives, is determined to reveal. There's a side-plot involving two mysterious gentlemen, and a famous unsolved riddle from Christie's own life. By the end, these different-shaped pieces have clicked pleasingly together, revealing a subtle moral about the secrets we keep and the suggestion that we need to shed them to be free.

Playing Christie, Lorraine Hooper's no-nonsense portrayal doesn't entirely conform to my mental image of the author, but in a way that might be the point: the story's very much about the difference between public persona and private reality. Both she and Samantha Drake (as Rutherford) do a fine job of selling the script's humour, with arch looks and exasperated glances often filling in thoughts that remain unsaid. The women's genteel cat-fighting provides the bulk of the comedy, and Agatha Christie fans – there were clearly plenty in the audience – will find no shortage of in-jokes to enjoy.

But there's a serious, sensitive side to the story too, as we see Christie and Rutherford develop a friendship almost despite themselves. Their lives echo each other in unexpected ways, and while Christie thinks she's digging into Rutherford's past, in truth she's shining just as bright a spotlight on her own. Their burgeoning trust is delicately portrayed – both women take their turns to share difficult stories, and the sensitive monologues are convincingly delivered by the two actors. It's not all introspection, though; one particular scene, where Christie eggs Rutherford on into a mild act of anarchy, is delightful in its conspiratorial naughtiness.

Linking these scenes together is an ambiguous figure, known only as "the Spinster" – a reference, of course, to Miss Marple herself. Sometimes, the Spinster acts as Christie's confidant; sometimes, she's pulling strings behind the scenes, bringing the author and the film star together. Kate Brennan is calmly magisterial in the role, though if I'm honest, I don't think Meeks' script gives her quite enough to do. It's not the players' fault, but at times I wasn't entirely sure what role her ambiguous figure was meant to fill.

This amateur company still has a few tricks and tips to learn; for example, some of the action was invisible from the back of the room, a problem that could be fixed simply by performing more scenes standing up than sitting down. But director Geoff Patenall uses the space cleverly, turning the doors set inconveniently at the back of the stage into a crucial part of the set.

Overall, Murder, Margaret and Me will please not just Christie aficionados, but anyone who likes poking their nose into a good mystery. It's an enjoyable and insightful production, delivered with both skill and heart.