Here is a puzzle or a riddle of a psychological movie, with distant echoes of Roeg’s Bad Timing or Antonioni’s Blow-Up. A brilliant and beautiful Hungarian neurosurgeon, Márta (Natasa Stork), abandons her career in the United States just shy of her 40th birthday and returns to Budapest. And why? Because she has met a handsome compatriot at an academic conference: János (Viktor Bodó) is a fellow surgeon who romantically arranged to meet Márta at a certain time and date at the city’s Liberty Bridge.

But János doesn’t show up, and when Márta tracks him down and confronts him, he merely says with an air of baffled politeness that they have never met. Márta takes a job in Budapest and rents a certain scuzzy apartment because it has a view of the now totemic, or cursed, bridge and begins to stalk János online, even uncovering a video of him as a child winning a singing competition with an arrangement of Schubert’s Trout Quintet. But her career still prospers, with brilliant diagnoses and masterly surgeries, which intrigue János. So what is going on? Is János lying? Is Márta delusional? Or is this her kind of obsession-based “magical thinking” – has Márta imagined what she wants in the future, and made an unconscious decision to behave as if it is the case, forcing the facts to rearrange themselves around her wishes, like iron filings around a magnet?

The paradox of the film’s narrative procedure is that it is shown from her point of view, not János’s, and yet it is Márta’s account that the audience is tacitly invited to challenge. The movie can’t quite match the drama – and the shock – of János’s denial of Márta at the very beginning, and the ending ties things up a little neatly. It is at once a relief and an obscure disappointment that the mystery is not left enigmatically unsolved.

• Preparations to Be Together for an Unknown Period of Time is released on 19 March on Curzon Home Cinema.