A large swastika was burned into the lawn of the Northern Virginia home of the director of the Federal Bureau of Alcohol, Tobacco and Firearms and a lifesize hooded effigy was found yesterday morning hanging from a nearby tree.

Bureau director Glenn R. Dickerson, 53, and his wife Mary were not at their McLean home at the time of the 4 a.m. incident, which is under investigation by the Fairfax County police.

Shortly after the incident a woman telephoned The Associated Press in Washington and said that the Communist Workers Party was responsible for the act. The woman did not identify herself nor disclose a motive.

The incident coincided with the opening yesterday in Greensboro, N.C., of testimony in the trial of six Nazi Party and Ku Klux Klan members charged with killing five members of the Communists Workers Party at a bloddy anti-Klan rally last Nov. 3.

Earlier this month a Greensboro newspaper disclosed that an undercover agent of Dickerson's bureau had infiltrated the Nazi Party and knew in advance of the caravan by the Klan that culiminated in the shootings. The agent, Bernard Butkovic, apparently failed to inform federal or local law enforcement officials of the caravan, although there is no indication that he knew in advance that violence would erupt.

Dickerson could not be reached for comment yesterday on the incidents at his home. A bureau spokesman declined to comment on the bizarre incident, saying he feared it might jeopardize the Greensboro trial.

Two bureau agents have been assigned to guard Dickerson's ranchstyle home in the Franklin Forest section of Mclean, a wooded neighborhood of $200,000 homes.

Police said yesterday that the flaming swastika and the effigy, which bore a red dot in the center of its forehead, apparently signifying a bullet hole, was discovered by a neighbor who called police.

The neighbor, who as not identified, reported seeing three persons get out of a car ignite the lawn with gasoline, string up the effigy and flee.