Federal and local law enforcement officials yesterday were still baffled but looking at the possibility that extortion is the motive behind a dozen death threats -- including a break-in and gunshot attack -- aimed at Sen. Edward Kennedy's top aide, Richard E. Burke, over the past two weeks.

Burke's mother, Anne, said yesterday in an interview from her Connecticut home that "it is inexplicable to us" why someone would be threatening to kill her son. She said no one had contacted the family seeking any money.

Burke, a 27-year old bachelor who lives in Northwest Washington, received a letter Thursday at Kennedy's office that made references to Burke's "wealthy father" and said, "Let's see how long your daddy's money can keep you alive."

That raised the possibility of extortion and brought the FBI into the case, to join the D.C. police department, Secret Service, Capitol Police and private investigators. The various agencies said they have no suspects.

Law enforcement sources said yesterday they believe one person is trying to frighten Burke rather than kill him, possibly a mentally deranged person or someone trying to act like one. The sources said there had been several opportunities to actually injure or kill Burke.

Private security guards were answering the telephone at Burke's fashionable Glover Park home. Late Friday night, Burke told a reporter that he could find "no rhyme or reason" for the attack against him.

"It's absurd. It's like a bad dream.T's very scary," he said. "I consider myself a nice guy. I go to church on Sunday and all that."

Burke is known among his coworkers as a man of substantial means. He lives in a spacious home on a three-quarter acre lot in the 3700 block of W Street NW.

Anne Burke said yesterday the family is "not fantastically wealthy." Burke's father, Robert E. Burke, is president of the American Electro Product Co. in Waterbury, and is an industrial broker.

Over the last two weeks Burke has received two written notes, a letter and seven telephone calls threatening his life.

The incidents escalated early last Sunday morning when someone tacked a death threat to his front door. Police checked the home and left.Then at about 4 a.m., as Burke was turning out the lights in his gymnasium and going to bed, his burglar alarm began emitting a low warning hum.

A minute later, someone climbed the stairs and began pounding on a locked door to a small sitting room that leads to his bedroom. At the same moment his preset alarm switched to loud, piercing screeching, Burke heard a thud at the door and hid in the closet.

The intruder fled, and when police arrived they found a butcher knife from Burke's kitchen stuck in the door.

Last Monday night, as he as getting into his BMW sports car, someone fired a bullet that shattered a rear window and came very close to his head, Burke said.

Burke said late Friday that he could not tell whether it was a person or group of persons who were threatening him.

The Secret Service entered the case Thursday night when a note, wrapped around a pipe and thrown against the side of Burke's house, threatened President Reagan's son, Ron, as well as Burke.

The note, which had a return address marked "SLA" -- a defunct California group of a few years ago, said in part, "We will get you for Kennedy and Ronnie Reagan for Reagan. We will get you and young Reagan, a liberal pig and a conservative pig. We know you have protection. It won't help. . . get rid of them or die."