So let me get this straight. I’m to star in a hit off-Broad-way show, in the plum role of a traumatised dad whose daughter has been killed in a car crash. It’s a prestige gig — the part has previously been played by Mike Myers, Frances McDormand and Christopher Eccles-ton. So where do I sign? Oh, hold on, there’s a catch. I get the part for one night only, and I have to perform it without ever having read the script or seen the show.

To most actors, this is the definition of fear — to be pitched onstage and into the audience’s glare without a clue what you’re meant to be doing. To Tim Crouch, it’s just the best way to tell the story of his two-person play, An Oak Tree . It is about bereavement, Crouch says, “about a character who has lost his way played by an actor who has lost his way”.

It has intrigued audiences, and alarmed a different co-star each night, from Edin-burgh via Lithuania to Man-hattan, where tonight I, a humble writer/performer shipped in from London for the occasion, will join Crouch onstage for the theatrical ride of a lifetime.

I arrive at the Barrow Street Theatre 45 minutes before the show. There’s a sandwich-board up with Polaroids of every previous participant. Male, female, black, white, young, old — anyone can play the part. (That’s part of the point.) There’s that legend of performance art Laurie Ander-son. There’s the Oscar-win-ner F. Murray Abraham and three-times nominee Joan Allen. Yikes.

“Relax,” says Tim. “The responsibility is mine. All I ask is for you to be open.” He hands me earphones, through which he will feed me my lines as we perform, and pages of script, from which I will read. And sometimes, says Tim, I will simply tell you what to say. And should I invent a character, I ask, or just be myself? Do you want me, in other words, to act ? “Every actor who comes in,” says Tim, in his Zen-like way, “they do their thing, and their thing is right.” Oh. OK. Thanks.

And later: “How are you feeling?” asks Tim. “OK,” I say. “Nervous?” asks Tim. “A little,” I have to reply — because this exchange has been scripted.

I’m onstage. The play has begun. “I’m being a hypnotist,” Tim announces, to me (and to the audience). “You’ll volunteer for my hypnotism act . . . because I accidentally killed your daughter with my car, and you think I may have answers to some questions you’ve been asking.” I furrow my brow, try to look vengeful. I might as well not have bothered. The Father’s most salient characteristic, I later learn, is not vengefulness, it’s that he thinks his daughter has been reborn as a tree.

“You’re doing brilliantly,” Tim says to me. But he has to: it’s in the script. The reassurance is not to be trusted. Tim likes to keep the second actor (and the audience) guessing. Am I playing the Father? Or a version of myself? Am I meant to be under hypnosis at this moment, or not? Tim hopes I’ll never be certain enough to start “acting”. “This piece will not let you settle into your old tricks and habits,” he says.

Having worked as an actor for 20 years, Crouch says later, he is frustrated with psychological realism. “By those moments that have been carefully honed by research and rehearsal, to the point where their liveness has been nullified.

“I’m interested in presenting a different model,” he says, “which is a totally unfinished piece of work.” What he wants to say to audiences — and actors — is: “Find the excitement in that random element.”

It’s not hard to. My heart’s racing. But I’m so focused on getting from one moment to the next, and not banging into the furniture, that I’ve no sense of what story we’re telling. (Later, looking back, it felt as if I’d been hypnotised.) Frequently, I read a line from the script and only afterwards understand it — and therefore (too late!) decide how I should have delivered it. But watching the next performance (with Walter Bobbie, the director of Chi-cago ), what’s fascinating is that acting can be just as honest, just as dramatically potent, even when (especially when?) the actor is only dimly aware of what he’s doing.

To Crouch, the changing-actor policy, far from being a gimmick, deepens the play’s exploration into representation and loss. The play is named after an artwork by Michael Craig Martin, a glass of water on a shelf which the artist invites us to see as an oak tree.

“The idea of loss,” Crouch says, “was the mainspring for conceptual art. If you have a fundamental loss, your previously held representation of the world has to change. Freud even says that the impulse to create comes from a sense of grief.” Witness the Father character in Crouch’s play, “who, in response to the death of his child, has taken a step towards madness,” says Crouch. “And on another level, he has created an achingly beautiful act of art by turning a tree into the girl who has gone.”

While in New York, Crouch is busy e-mailing British actors and agents, drumming up co-stars for his London run. (Actors are paid to take part.) He thinks of the play as actor-proof. “In terms of its ideas, it’s rock solid. And if, at any given performance of it, there isn’t a connection, if the two actors don’t work together rhythmically, that’s OK.” The co-stars needn’t be box-office draws — although Barrow Street Theatre, against his will, has advertised in advance the schedule of second actors. (This won’t happen in London. The co-stars will be a surprise. Think of it as an experimental Play What I Wrote .)

Some actors have cried all the way through An Oak Tree . Others have refused to engage. “Frances McDormand said it was like mainlining a dose of theatre into her system,” he says, “like having the rehearsal, the first night and the last-night party, all in one evening. But other actors find it really unnerving.”

I did, but I also found it provocative and thrilling. My photo is now pinned on the sandwich-board, keeping good company between the film star Lili Taylor and sit-com icon David Hyde Pierce.

Have I earned my Polaroid place among those acting greats? Over to Tim.

“What you did was what you did,” he says, keeping me guessing to the very last, “and it was great.” Does he mean that? Just let me check the script. An Oak Tree opens at the Soho Theatre, W1, on Wednesday (0870 4296883; www.sohotheatre.com )

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