Bugging is as fatal to Arthur Miller's "The Archbishop's Ceiling" as it was to Richard Nixon's White House.

In the new drama, which opened Saturday at the Kennedy Center's Eisenhower Theater, a microphone is picking up what tbe characters are saying. We know the character know this because they pointedly address the chandelier or, to get out of its hearing, stalk out - with time consuming pace - to what may be a hallway to say what they really mean. Do they really mean it? Is the hallway bugged? If not, why not? Or is there, maybe, not a mike in the chandeliler

That is to be sure, part of the police state atmosphere Miller is creating for his suggestion that to transpplant a writer from his roots, however constricting the regime around him, can kill the writer's gift. Offered the possibility of escape from a police state is it more courageous to stay?

Such a question is worth raising and one senses that this play is the residue of Miller's years as president of PEN, the international writer's association.

But, oh, how long it takes to get to the matter through the thickets of Act 1 exposition Adrian, a rich, famous American writer is in an unspecified European capital. Is his purpose to influence Sigmund, a writer whose recent letter about freedons has been a sensation in the United Nations? Or is Adrian just poking around old memories knowing that Maya is good for a quick, not one-night stand?

Maya, who tells a shadow go-between that she'll do anything to keep from being sent back to the factory, is a beauty of infinite experience. She apparently is an actress, a writer and a bundle of catnip, presently the posession of Marcus, a "former good friend" of Sigmund. Would Marcus prefer the national turr rid of such a professional and personal rival as Sigmund? She has had some liason with Martin, a critic who serves both state and art. How serious is Sigmnund about Maya?His unseen wife, Anna, doesn't know that in government hands there is a picture of him and Maya in the nude. There is also on stage Irene who has nothing to do with the plot except a remote connection with the BBC, can't understand the language, only wants to dance and is here, I assume, to show that Marcus, whom the government allows to travel, will pick up whatever he can get.

By choosing bugging as a theatrical device, Miller is forced into purely technical choices which belabor his moral concerns, taking unconscionable time. For comparable stories on film, the director would flash close-ups of hidden mikes or lead his characters out to the countryside or onto an open boat.

The Eisenhower's four-week run - Miller latest effort since his "The Creation of the World and Other Business" of two years ago - is the play's first outing. There are no immediate plans for critical New York exposure, good news both for New York and Miller, who now can go back to Square One.

As for the players, John Cultum gives Sigmund a sense of inner preoccupations, longing only to do his work and validating the thesis that elsewhere he might not be able to write. Douglass Watson's Marcus has assurance and passion, suggesting reasons for at least partial collaboration. As Adrian, Tony Musante has little to work with except his hands. In Maya, Bibi Anderson has a role demanding the combined skills of Colleen Dewhurst, Etherl Barrymore and Sarah Bernhardt, looking lovely and, not unnaturally, puzzled.

Constricted by the need for acting areas at both sides of the stage. David Jenkins' setting and Arvin Brown's staging seem adequate. The proglem lies in the script, which doesn't really begin until Act. II, by which time we feet it's Friday afternoon, when fresh plotlines are being threaded into the soaps.