The four-night run of "Marmara the Gypsy" at the Kennedy Center last week has caused some people to wonder whether the center exercises any artistic control over groups that rent its facilities. The answer is no. Laura Longley, director of communications for the Kennedy Center, said a prospective renter is checked out financially. But to base a rental on potential artistic merit not only would be impractical but could be an abridgment of First Amendment rights, she said. The cost of renting the theater in the center usually discourages amateurs. The tariff, for example, where "Marmara" played starts at $1,250 for one evening performance, plus the cost of union stagehands, which begins at $250 for two men for four hours, plus the cost of house managers, ushers and other personnel.

Should there be a case of bad taste -- as opposed to bad art -- Longley said, the center's trustees would have to decide whether the show would go on. In the 15 years the Kennedy Center has been operating, there has never been an occasion for them to make that choice.

The advertisements for "Marmara," for which most tickets cost $35, carried what appeared to be an endorsement from local talk-show host Maury Povich. Povich said he had not seen the show, but had had some performers from it on "Panorama." He said he had neither authorized the use of his name nor endorsed the show.

Independents who lease a Kennedy Center theater are not allowed to use the center's name as an imprimatur in their advertisements or future billings, Longley said. Fichandler Wins Award

Zelda Fichandler, founder and producing director of Arena Stage, is to receive this year's Common Wealth Award, a prestigious gift awarded by the estate of business executive Ralph Hayes. Previous winners have included Laurence Olivier, Tennessee Williams and Stephen Sondheim. The award comes with a nice hunk of cash (about $16,000) and a black-tie dinner, which this year will be held in Washington instead of Sardi's in New York.

"It's nice to be recognized by people who understand what you're working for," Fichandler said recently. "It's a form of societal love, and who doesn't like that? And I think people of Arena rightfully feel that some of the pride and pleasure is theirs. Call it 'gilt by association.' But what awards really mean is that you have to keep on earning them. As Beckett says, you have to keep on keeping on."

Meanwhile, Arena has released its annual report, which should add to its reputation for sound fiscal management. The balance sheet shows a surplus of $100,000, which will go into the operating reserve fund, which allows the theater to produce potentially unpopular "risk" shows without facing financial ruin. Expenditures totaled $6.4 million and income was $6.5 million, with the box office bringing in $4 million. The only show that sold at less than 80 percent capacity was "Real Estate"; the best seller was "Tartuffe" at 92 percent. The largest categories of expenditures were payroll at $3.9 million, advertising and public relations at $830,156 and production expenses at $572,935.

Of a projected $6 million endowment, $4 million has been raised, with the aim of providing a steady source of income in future years. The theater is financially stable enough to have hired a resident company for 52 weeks a year for the first time, and expanded rehearsal time from four to five weeks per play. However, salaries for nearly half the staff are still $15,000 a year or less, which Arena officials say reflects the low esteem in which most of society continues to hold the arts. 'Iguana' to Fold

The Jeanne Moreau production of "The Night of the Iguana" now playing in Baltimore will end its run there (on Nov. 10), the producers announced last week. The Broadway opening has been canceled for "artistic reasons." Fred Walker, one of the producers, said the "fine-tuning and the need to polish is not coming together." He did not mention the terrible reviews. Coming Attractions

The Stratford Shakespeare Festival will bring its productions of "King Lear" and "Twelfth Night" to the Warner Theatre in January; Douglas Campbell will be Lear . . . The Flying Karamazov Brothers will return as part of the International Arts Festival at George Mason University in March, along with the touring arm of Minneapolis' Guthrie Theater doing "Great Expectations" . . . Doug Henning and his magic show come to the Warner Nov. 20 . . . "Corpse!" opens at the Morris Mechanic in Baltimore Nov. 12 . . . Irish actress Claire Mullan does a one-woman show at Alexandria's Lyceum Nov. 17 . . . Donald Driver's new play, "A Walk Out of Water," which he will direct, opens at the Studio Theatre Nov. 20 . . . A new play about terrorism by University of the District of Columbia student Bill Quinn gets a production by the school's theater department starting Thursday . . .