Twelve years after an Orson Welles radio drama made some Americans think Martians had landed in New Jersey, citizens of Wisconsin were led to believe that there had been a Russian invasion on 1 May, 1950. Though almost certainly inspired by that first fiction of breached borders, this second hoax was not broadcast by a Hollywood star but organised by the state branch of the veterans’ organisation, the American Legion. This was presumably due to fears that people were not taking seriously enough the communist threat to Truman’s America from Stalin’s Soviet Union.

On that midwest mayday in the middle of the 20th century, the town mayor and police chief were dragged from their beds by “reds”, the library was purged of subversive texts and diner menus substituted potato soup and black bread for the usual meats and sweets. Although this was an exercise in pretence, a real-life local leader was dead by the end.

The fake takeover is a true story, but the records are sketchy. And so The Mosinee Project – a three-actor piece created by the Counterfactual company – soon moves from research (recorded interviews with living witnesses) to speculation, through imagined rehearsals for the May Day and multiple versions of some scenes.

Fascinatingly, two of the creators of the mock occupation were themselves former communists, allowing writer-director Nikhil Vyas fun with the idea of whether disguise can morph from a lie into a life. Are some Wisconsin Republicans possibly entering too enthusiastically into the commie cosplay? Might one of the ex-reds only be pretending to have embraced American democracy?

The three actors – Camilla Anvar, Jonathan Oldfield and Martha Watson Allpress – play multiple roles with impressive fluidity of nationality and gender. At a time when the reality of the “red scare” is again the subject of debate in Europe, The Mosinee Project has topical resonance as well as historical fascination. But there is sometimes frustration in not knowing what actually happened. This entertaining 70-minute exercise in levels of reality leads us to other sources on the story, and Counterfactual might usefully explore a more fully fictional telling.