In 1959, Burt Pugach paid three men to throw lye in the face of his ex-girlfriend, who was disfigured and largely blinded. In 1974, on Pugach’s release from prison, she married him. Dan Klores’s documentary charts the course of their relationship, and in so doing shows just how bizarre human behaviour can be.

The pair met in the Bronx in 1957. Linda Riss was a beautiful 20 year-old; Burt was 10 years older, a womaniser, film producer and, unhampered by moral scruples, successful negligence lawyer. He had a private plane, a Cadillac and part-ownership of a club, and the working class Linda lapped up the money and the glamour. But, however dazzled she might have been by this sudden introduction to the high life, she couldn’t be prevailed upon to have sex without marriage, which put Burt in rather a difficult situation, seeing as he already had a wife. He stalled, made promises, and faked some paperwork to make it look like he was applying for a divorce; despite discovering it was all a lie, and despite Burt’s spiralling paranoid jealousy, Linda agreed to go to a doctor to prove she was still a virgin. It took her until 1958 to finally tell Burt she’d had enough.

She soon fell for another guy, Larry Schwartz, who she met in Miami Beach. The psychotically obsessed Burt harassed and threatened her; Linda reported his behaviour to the police but was told there was nothing they could do. It was in June the following year, when Burt found out that she and Larry had got engaged, that he resolved if he couldn’t have her, no one would, and hired men to go to her house and throw acid in her face. Linda spent three months in hospital.

During his trial, Burt smashed his glasses and used them to slash his wrists in a bid to get declared mad. After a lengthy psychiatric examination he was judged sane and sent to prison, where he took pride in getting his fellow inmates released on legal technicalities, and wrote long letters to Linda. Fourteen years later he got parole, and proposed to his victim on air while being interviewed for a news programme.

By this point, Linda was poor and alone. Larry had swiftly deserted her after the attack, and she'd given up dating men, realising her chances of marriage were slight: one keen suitor fled without a word when he saw her without her sunglasses. The year Burt was released, despite the vitriolic hatred she had always professed, Linda agreed to marry him. In 1996, when Burt was accused (and acquitted) of hiring someone to kill his mistress, she was a character witness for the defence.

Burt and Linda’s lurid, chaotic relationship has generated violent squalls of media excitement over the years. Dan Klores chooses to tell it straight, in a talking-heads style documentary. This format initially makes the film seem rather dry, albeit intercut with some beautiful shots of Fifties New York; it quickly becomes anything but, chiefly because of the fantastic characters he finds to speak to: Burt’s business partner – “ They say even Hitler had friends”; his extraordinarily ugly and obese former secretary, with whom he had an affair, and who says with no hint of irony that he only hired her for her beauty; the female police officer assigned to protect Linda who recognises her charge’s loneliness and neediness and sets up a meeting for her and Burt; and a freakshow of other bit-players, who all throw out unintentionally hilarious one-liners. Klores also structures his material well, tipping us from one moment of inexplicable insanity to the next.

So sensationalist and fantastical is the story and its players that the film needs this stripped down, unintrusive approach to remind us that it isn’t fiction, and to give us, as viewers, the space to attempt to understand its subjects. How could Burt become so obsessed, and act so despicably, apparently without feeling any remorse? And how could Linda not only marry him, but publicly defend him when he cheated on her? We can guess at answers. Monumental self-delusion would be one. Both had difficult childhoods. Linda is scared of poverty and loneliness: her life ambition is to be beautiful, glamorous and married, but after the attack she is, in her words, “damaged merchandise”, and subconsciously normalises Burt’s actions out of self-preservation and pride. Burt is a repulsive, selfish, lying, self-aggrandizing worm. But as the film leaves them quarrelling outside their local diner, you get a sense that they do, somehow, love each other – that they have made each other be ‘made for each other’.

Is it wrong to turn these characters’ captivating, car-crash lives into dark comedy, to give them more limelight with which to fictionalise themselves, to laugh at what is essentially a tale of abuse? Aside from the fact that just switching off the media lights now would achieve little, Klores doesn’t twist his material into a Hollywood-style redemption narrative. By simply allowing his protagonists to tell their story – unwitting humour and all – without making judgements or offering facile explanations or labels of his own, he demands we recognise the mysterious, strange complexity of human psychology.