The U.S. Court of Appeals, asked to referee a bureaucratic feud over limousine service at Dulles International Airport, ruled yesterday that the Washington Metropolitan Area Transit Commission has jurisdiction over public transportation service there.

While the court decided in favor of WMATC in its dispute with the Federal Aviation Administration at Dulles, it also urged the two agencies to balance their dual powers at the airport in favor of the traveling public.

Judge Carl McGowan, in a 15-page opinion, wrote that the court had the impression that WMATC and the FAA had made it a point "not to deal with one another -- much less to cooperate . . ."

McGowan, who described this attitude as "dangerous," said "neither agency should use its authority to frustrate the efforts of the other." The FAA is the proprietor of both Dulles and Washington National airports. The WMATC certifies various carriers to provide ground transportation out of both airports.

The dispute decided yesterday arose in 1976 when the FAA refused to contract for service with Executive Limousine Service Inc. which had been certified by the WMATC to provide service from Dulles to the Hyatt Regency Hotel on Capitol Hill. The FAA said it had awarded that exclusive contract to the Greyhound Corp.

The appeals court ruled, however, that Congress, when it created the WMATC in 1960, intended that it regulate the transportation of passengers from Dulles. The FAA agreed that all carriers had to be certified by WMATC. But it argued unsuccessfully that it had the right to deny contracts when, as in Executive's case, exclusive right to service had been awarded by FAA to antoher carrier.

McGowan wrote that while the FAA does have the authority to contract with carriers, it cannot deny a contract to a carrier certified by WMATC.

The FAA may offer its expert opinion about the number of carriers needed at Dulles, the court said, but the ultimate decision belongs to the WMATC.