This low-budget indie set in the dark heart of the rural English suburbs begins with a woman plunging an eight-inch kitchen knife into her husband’s head. The tone that director Stephanie Zari is going for seems to be that blend of violence and black humour that Fargo and Killing Eve make look so easy. But Zebra Girl’s quirky comedy is not quite distinctive enough, and the script lurches iffily into serious issues of child abuse and mental illness in the second half.

Sarah Roy plays the murderer, Catherine, who grabs a knife from the cutlery drawer after catching husband Dan (Tom Cullen) watching unpleasant porn at 3am in the study of their country pile. A shrieky horror movie score blares as she does the deed and afterwards she wraps a fluffy pink towel around his head. The next morning, she calls in childhood friend Anita (Jade Anouka), who is shocked – but not exactly surprised – to walk in on a murder scene. It turns out that Catherine’s plummily posh private school accent and Tory chic fashion taste (pink cashmere knits and pearl earrings) are an affectation. What’s also clear is that she’s a psychopath without a trace of conscience. “Help me bag this bastard up,” she snaps at Anita. Even with the deadpan one-liners she’s not an interesting or layered character.

In flashback we see Catherine and university lecturer Dan meet and fall in love. On their first date she is manic and awkward, telling him about her dark past. He’s taken aback, but not put off. “You were a national story,” he marvels. That past emerges in flashback, too, in scenes showing Catherine as a little girl (played Daisy Mayer), then as precocious teenager (Isabelle Connolly) being questioned at a police station. For me, the cartoonish violence and flippancy of the adult bit belongs to a different film from some of the upsetting episodes elsewhere.

• Zebra Girl is in cinemas from 28 May.