MIAMI (AP) _ A U.S.-registered sailboat with three people aboard was reportedly shot at and taken into custody by a Cuban patrol boat, Coast Guard officials said today.

''We got word from the State Department that the Cubans told them they have released the boat,'' Coast Guard spokesman Jim Simpson said.

A passing merchant ship reported to the Coast Guard late Thursday that shots were fired across the bow of the 48-foot sailboat Tranquility near Cayo Guajaba, on Cuba's northern coast, Simpson said.

The Tranquility told the merchant ship by radio that it was then taken in tow by the Cuban boat, Simpson said.

Crew members were two men and a woman whose names have not been released, the spokesman said.

The whereabouts of the U.S. citizens and the boat were uncertain, Simpson said. ''We are going to get a plane up to see if we can locate them and talk to them.''

Meanwhile, a Havana radio station reported today that a U.S.-registered boat carrying 7,700 pounds of marijuana was seized in Cuban waters and its four crewmen taken into custody.

The Cuban Coast Guard captured the ''Mary'' on Feb. 6 near the Las Tunas province area in northeastern Cuba, reported a Radio Rebelde broadcast monitored in Miami.

The arrested crew members were identified as Puerto Rican-born Ivan Lancharte Ramiro, and Cuban natives Lazaro Perez Garcia, Inocente Hernandez Lores and Roberto Iglesias de Rojas.

Radio Rebelde said Perez and Hernandez left the island illegally in 1979 and that Iglesias left in 1980. All four were arrested and detained and the marijuana was burned, the radio said. The report did not say whether the Cuban natives were U.S. citizens.