Americans may be able to play Hamlet, Oedipus, King Henry VIII and Mephistopheles, among other foreigners. But they cannot play Liza Doolittle in one American production of "My Fair Lady."

That is the effect of a controversial decision made yesterday in New York.

British actress Cheryl Kennedy, who is virtually unknown in the United States, was found "uniquely qualified" to play that role opposite Rex Harrison in a revival of the Broadway hit of the '50s. The show will open in New Orleans next September and will tour American cities (perhaps including Washington) for nearly a year before beginning an open-ended run in New York in the summer of 1981.

Actor's Equity, which had challenged the casting of Kennedy -- insisting that there were American actresses qualified for the role -- was stunned by the decision.

"It defies all logic" said Don Grode, an Equity spokesman. "apparently, she was permitted to come in under the provision which allows entry to an alien actress who can provide 'unique services.'

"This means that in the arbitrator's judgement, there is no American actress qualified to play the role. In a play as old at "My Fair Lady," and one that has had hundreds of productions in this country with American actresses, that decision is amazing."

Producer Mike Merrick, reached by telephone at his Los Angeles office, said that Kennedy was, in fact, the only qualified actress, in his opinion. "We auditioned more than 50 finalists and it would not have worked with any of them." Merrick said. "The Americans we auditioned were either wonderful singers or good actresses, but they couldn't capture the unique quality of that character -- the flower girl and the guttersnipe with the cockney accent and the beautiful voice."

Arbitrator Daniel Collins, a professor at New York University, refused to comment on his decision. "I can't say a word," he said. "It's a private arbitration."

Grode complained that "because of this award, the role has been denied to an American actress."

But Merrick argued. "This production will be providing a lot of American actors with work, besides giving the American public an authentic product." Of Kennedy's qualifications, he said: "She has played in about eight musicals in London's West End, she was born in North London; both her parents are cockneys and she sings like a lark."

Harrison, who is just as British as Kennedy, was not challenged by Equity, in effect because we've grown accustomed to his face. "Nobody would dream of challenging Harrison," said Grude. "He qualifies easily under the clause on star status."

This clause in the Equity regulations embodies rules written by the U.S. government concerning the immigration of performing artists. To qualify legally as a star, an actor must be able to demonstrate "current, widespread acclaim and international recognition" or show prizes or awards for excellence, show playbills in which he or she has been given star billing or demonstrate a level of income compatible with his or her claimed level of ability. Apparently, this clause also covers Irishman Milo O'Shea, who -- with a little bit of luck -- has been cast as Mr. Doolittle without a challenge from Equity.

Harrison, who has not previously worked with Kennedy, flew up from Florida where he was playing in "The Kingfisher" to testify for her at the first hearing on the case held by Equity, Merrick did not say that Harrison refused to play with an American actress, but when he was asked what he and his partner, Don Gregory, would have done if Kennedy had not been cleared for the role, Merrick said:

"We would have tried desperately to find another young English actress who is legally acceptable to Equity and whom Harrison could have worked with."

On Kennedy's qualifications, he said, "we fulfilled Rule 3b of the Equity bylaws, about artists of special and unique talents. We proved that Miss Kennedy had such talents, because other ladies who had played Liza Doolittle in the past had not been able to catch the unique accents of the cockney dialect."

The dispute was given added point by the chronic difficulty American actors have in securing clearance to play in British theatrical productions. British Equity, unlike its American counterpart, consults directly with the government office that decides such questions.

"This kind of a situation," Grode said, "would never occur in the United Kingdom because British Equity is better able to protect its members."