From the beginning, law enforcement investigators concluded that there was something wrong with Richard Burke's story.

Yet, he was the top aide to Sen. Edward M. Kennedy (D-Mass), the chief of his 60-member staff, the manager of his campaign airplane, and when he complained that he was the target of death threats, investigators from the D.C. police, Secret Service and FBI listened carefully -- even though they instinctively felt from the start that Burke was perpetrating a hoax.

"There was no doubt that he was doing it to himself," said one investigator, "but when you sat down and talked with him you come away shaking your head. He comes across as an intelligent, articulate young preppie with all the right schools, the right family, a kid who has power . . . angelic, cherubic with a button-down oxford shirt -- so far removed from Mr. Slick, from any kind of con. It was quite an acting job."

Investigators conducted a month-long investigation into alleged telephoned and written death threats, into a shooting and a break-in. But the hints that Burke was setting up himself were powerful: a bullet hole that was simply too large, mailed death threats that mysteriously arrived at Burke's home undetected despite 24-hour surveillance, typed death threats composed with precisely accurate verb tenses contrasting sharply with simple words that seemed consciously misspelled.

Because of Burke's "authenticity", as a source close to the case put it, and, of course, his position, he was noted asked whether he would submit to a lie detector test. At least not at first, and law enforcement officials looked hard into his story. What they found, pieced together in a series of interviews yesterday, was a continuing series of holes in Burke's version of events.

The 28-year-old bachelor filed a complaint with police alleging that someone shot at him on the night of Feb. 9, while he sat in his $20,000 BMW sports car in the driveway of his fashionable Northwest home. But no one in the neighborhood had reported hearing a gunshot. And the bullet hole in the windshield was the size of a baseball.

Investigators concluded that had the car been shot on the spot, the bullet, at the velocity it travels, would have made only a small hole. "You don't get a hole as big as that," one detective noted, "Until you drive the car,"

Burke complained that in the early morning hours of Feb. 8, an intruder broke into his house, grabbed a butcher knife from his kitchen, raced up the stairs and stuck the knife in his bedroom door before fleeing when a timed burgular alarm went off. But investigaors wondered how an intruder would be familiar enough with the house to execute all this in the few seconds. The complaint, however, initially brought police into the case.

The Secret Service joined in after Burke complained that on Feb. 12 someone had thrown a pipe with a threatening note wrapped around it against his house. The typed note read 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."

But investigators believed that this and other written threats, appeared to have been written by someone intelligent who tried to sound uninteliigent. Simple words, like "said" was misspelled, while more difficult words, like "liberation" were not and the grammar was essentially correct. "When someone intelligent tries to write a letter that sound unintelligent, he's got a problem -- it sounds intentional," said another source close to the case.

While Burke surrounded himself with 24-hour private protection, he continued to go to parties and carry on his social life, which investigators found odd.

Moreover, one of the threatening letters claimed to be from the defunct California radical group, the Symbionese Liberation Army. But investigators checked and found no recent activity by that group. Burke claimed at another time that a threat had been placed in his mailbox, but law enforcement surveillance had seen no such delivery.

At the end of last month, law enforcement officials finally revealed their suspicions, confronting Burke with what he had said and contrasting it with what they knew. Burke left to get a lawyer. When he returned, Burke acknowledged that he was responsible for the incidents.

He went on leave March 1, appearing in the office from time to time, and resigned last Thursday.

Although law enforcement officials concluded their case and referred it to the United States Attorney's office here on March 3, Burke did not inform Kennedy of his actions and decision to resign until last Wednesday.

Most of the staff did not know about the resolution of the incidents until a Washington Post reporter called Thursday to ask if it was true. A staff aide said yesterday that Kennedy had planned to announce the resignation on Monday, after Burke had informed his family. Instead, the announcement was made at the close of the day Thursday. Many staff members were stunned, said staff aides.

The U.S. Attorney's office is considering whether to prosecute Burke on charges of filing false information with law enforcement officials and illegally discharging a firearm.

Still unexplained is why Burke did it. He seemed to be at the peak of his career. He had access to the country's best-known senator, control of his staff, a busy social life that included trips to Martinique and the Bahamas, large parties at his Glover Park home, expensive evenings at Georgetown night spots.

In his brief letter of resignation, Burke cited only the pressures of the job to explain his behavior. He said he was seeking medical help.