In seeking to extend the American Ballet Theatre repertory in a multiplicity of stylistic directions all at once, the company's relatively new artistic director, Mikhail Baryshnikov, is pursuing long-established ABT traditions. The company has always regarded itself as a "living museum" of ballet, old and new, and has engirded a central core of made-in-America products with importations from Slavic, Latin, Scandinavian and many other sources. Hence the company's premiere performance of Roland Petit's "Carmen," at the Kennedy Center Opera House last night, was a logical extrapolation from ABT's history.

The result, however, had its equivocal sides. The production, based on Petit's original for Paris in 1949 with Antoni Clave's spectacular designs reproduced by John Jensen, is dazzling to look at, and was so last night despite the considerable technical snarls this first attempt ran into. The dancing, from Natalia Makarova in the title role, Baryshnikov as Don Jose, Lisa de Ribere as a bandit girl, Victor Barbee as Escamillo, and a splendidly drilled supporting cast, was as superb as could be. But the ballet itself is something else again -- for all its patent flamboyance and tempestuousness, one couldn't help but wonder whether this brand of melodramatic hyperbole remains viable in 1981. Time was when people found Petit's idiom pretty hot stuff; nowadays, the temptation is to smile.

The ballet, using Bizet's familiar score, compresses the operatic action into five blunt, feverish scenes. The first, in a sordid Seville square, introduces Carmen the cigarette girl in a brawl with a co-worker, and then Don Jose, a sort of magistrate who drops his sense of duty under Carmen's erotic spell. A steamy, low-life tavern scene follows, in which Don Jose dances a fiery solo to the Habanera and is further tempted by Carmen's teasing. Then comes a morning-after scene in Carmen's flat; Don Jose's passions are rekindled in a lascivious duet. The ensuing street scene, in which Don Jose is needled into a killing by Carmen and her outlaw companions, is obscure and needs motivic clarification. The finale, in front of the bullring, gives us Carmen tossing over Don Jose for the foppish toreador Escamillo, and getting herself stabbed by the jealousy-maddened Don Jose in the bargain.

The French have this reputation of being naughtier than the rest of us; it goes back to Rabelais and Balzac and all that, and Petit is a modern exemplar who also goes in for a kind of theatrical floridity that is characteristically Gallic. If Carmen is a tease, Petit is her adept pupil, and he has practiced the craft in nightclubs, in Hollywood and on the international stage. The trouble is that in the wake of the '60s' sexual revolution, Petit's idea of the risque looks, well, a bit silly, and the Carmen yarn, which was borderline ridiculous to start with, only exaggerates the dated aspects of Petit's dramaturgy. "Carmen" is an authentic period piece, and Petit's clever mixture of apache dance, flamenco and ballet retains a skillful veneer. On the whole, though, the ballet today comes across as a howler. Even the persuasively blistering dancing and acting by Makarova and Baryshnikov can't save the characters from seeming like caricatures.

Elsewhere on the program, Alexander Godunov proved surprisingly impressive in his smoldering, understated debut as the poet in "La Sonnambula."