Parade is a newish (1998) American musical about the real-life trial, conviction and lynching of a Jew called Leo Frank in Georgia in 1915. His alleged crime was to have raped and murdered a 13-year-old called Mary Phagan. Musicals about paedophile killers don’t come along every day, it’s true, and on Broadway the show ran for only 84 nights. So, if this is your kind of thing, you’d better hurry.

Much of the piece is essentially a courtroom drama with added song-and-dance routines. Trial by television is one thing, but trial by musical? The danger of trivialising a criminal case that was both grotesque and significant in the history of the American South is considerable. Add to that the fact that it was a black man’s testimony before an all-white jury that convicted Frank, and the ironies only multiply. Partly due to the very simplicity of the form, however, Parade fails to acknowledge them. Musicals don’t handle sociohistorical complexities too well, and the political shenanigans behind Frank’s conviction are grossly simplified into stock characterisations of ambitious senators and slimy attorneys.

As for the crime and its aftermath, this is a pretty cosy version. In reality, Phagan was left violated in a cellar, bleeding and black with coal dust; the Atlanta police department was notoriously primitive and corrupt; and, after Frank’s death, crowds gathered to mutilate his body and take bits of the tree and rope home by way of souvenirs. Human nature was seen at its worst throughout the case, and you’d expect a musical about it – if there must be a musical about it – to cut through any fluff and schmaltz to the truth and horror with incisive wit, raw honesty, even black (or Jewish) humour.

Instead, centre stage is the loving marriage between Leo and Lucille Frank. The more the case progresses, the more she loves him. Is this credible? Might she not have felt more doubt and disgust? The writer, Alfred Uhry, also seems pretty sure he knows who really dunnit: the black guy, Jim Conley. Nearly a century later, without forensics, that’s quite some self-assurance.

The cast do their best, and a few are excellent, especially Shaun Escoffery, as Conley, putting a magnificent singing voice to good bluesy use, and Bertie Carvel, as Leo Frank, slowly transmogrifying before our eyes from almost wholly unlikeable creep – humourless, finicky and cold – into something rather more sympathetic. The designer, Christopher Oram, as usual comes up trumps, with a huge, haunting sepia backcloth from which ancient faces peer out, our forefathers gazing down solemnly upon proceedings, upright and unsmiling. And the director/ choreographer, Rob Ashford, has devised a genuinely chilling dance of clownish horror for when Frank is sentenced to death. He and Lucille cling together as if both sentenced,while the court erupts in a vicious celebratory hoedown, circling around them and whooping with glee at their despair. It’s a moment both ghastly and revelatory. Yep, that’s how people sometimes behave. Look at it long and hard. Then check your mirror.

Too little of the show is up to this level, however, and any pretensions it may have to being a brilliantly incisive study of racial tensions and hatreds are to be strictly disregarded. The music and lyrics, by Jason Robert Brown, are tuneful, inventive and sometimes married together with the deftness of Sondheim. But there are clunkers, such as the Confederate soldier singing goodbye to his gal in 1862, with the immortal line: “I miss you already.” And sometimes they’re completely baffling. What are we to make of songs about the good ol’ red hills of Georgia? What exactly is the purpose of a song praising Dixie, sung by a partly black chorus, hymning the joys of growing cotton and “A way of life that’s pure/ A truth that must endure / A land where honour lives and breathes/ (And Jews and nigras hang from trees)”? I made that last line up, but you can see why. Is this stuff ironic, or is it really cornier than corn pone? I still don’t know, but I fear the latter.

Quite a while before the end of this near-three-hour show, you begin to feel that serious issues are being ducked and glossed over, and that continually breaking into jolly song-and-dance routines in the midst of a corrupt trial about a paedophile rape and murder is not quite, as we would say nowadays, appropriate behaviour.

Despite a valiant production, the end result leaves you feeling more than a little queasy.

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