A 20-year-old man smuggled a rifle into the heavily guarded State Department yesterday, made his way to his mother's crowded office, killed her with a flurry of shots and then fatally shot himself in the head, D.C. police said.

No one else was injured in the noon shootings, which occurred about 120 feet from Secretary of State George P. Shultz's seventh floor office, where Shultz was working on the TWA hostage crisis in Beirut, a State Department source said.

"This was not a terrorist incident," said State Department spokesman Bernard Kalb, adding that it was "in no way" related to official State Department business. Kalb and D.C. police said there was never a threat to Shultz or any other senior department official.

D.C. police said the incident appeared to be family related, stemming from longstanding problems between mother and son, but that they didn't know what led to the shootings. The mother had recently complained to police that her son had assaulted her, and she stayed for two weeks in a shelter for battered women to escape his attacks, according to authorities.

The man, armed with a gun and a knife, was able to get to the seventh floor of the massive Foggy Bottom office building by using a State Department "dependents' pass," issued to family members of State Department employes and which permits entrance without going through metal detectors or being searched, police sources said. The gun, a break-down .22-caliber rifle, was hidden in a canvas bag, police said.

The incident occurred in the offices of State Department Counselor Edward J. Derwinski, according to Deputy Chief Alfonso Gibson, head of the D.C. police's Criminal Investigation Division.

Police identified the dead woman as Carole Doster, 44, and her son as Edward Steven Doster, whose address was uncertain last night. Carole Doster, of 5055 Seminary Rd., Alexandria, had worked as a secretary in Derwinski's office since last September, according to a State Department spokesman.

Both were pronounced dead on the scene by the D.C. medical examiner. Police sources said that Carole Doster had been shot several times in the body and the head, and that her son was shot once in the head.

Another source close to the investigation said that there was a "good indication" that the man had also stabbed his mother, which would be determined by an autopsy.

The incident prompted widespread concern and swift criticism of security procedures at the State Department, which within hours of the shootings instituted new guidelines for admitting visitors to the building at 22nd and C streets NW.

The sources also said that several weeks ago the mother had told the director of security at the State Department that her son had threatened her and asked that his special pass be taken away.

"She had sent an urgent, written communique requesting that his family pass be revoked," according to one police official. "There is no indication that they [State Department officials] had acted on the letter," another police official said.

The official said the State Department had prepared a memorandum on the mother's request, dated Thursday, but that the department "hadn't had a chance to put it into circulation." The source said there was "no indication" any steps had been taken to rescind the son's pass or bar him from the building.

However, the source said, Carole Doster "may have been running around with a photograph of him telling security people to please don't let him in."

State Department spokesman Sondra McCarty said last night that on June 19 the office responsible for building passes received a request dated May 30 from Carole Doster, asking the department to revoke her son's dependent pass.

"Unfortunately, the incident occurred before instructions could be forwarded to the [Federal Protective Service] guards," McCarty said. Asked why the processing took so long, she replied: "We don't know. That's part of what we're investigating."

The sources said that Edward Doster, carrying a canvas gym bag that concealed the rifle, walked in the main diplomatic entrance on C Street, dressed in a yellow T-shirt and Army-style fatigue pants and took an elevator to the seventh floor, sometimes known as the State Department's "corridor of power," which also houses the offices of Deputy Secretary-designate John Whitehead and Under Secretary for Political Affairs Michael H. Armacost.

There, he entered a men's restroom and put together the rifle, described by one police source as the kind that breaks down and fits into the stock.

As he left the restroom and walked down the hall toward his mother's office with rifle in hand, police and State Department sources said, several persons saw him and notified security, which immediately sealed off Secretary Shultz's office.

The man entered a small office his mother shared with two other secretaries, and after "some conversation," shot and killed her before shooting himself, a police spokesman said.

An employe on the seventh floor, who did not want to be quoted by name, said that during the shooting persons in the small office screamed and dived under desks, and that afterward someone kicked the rifle out into the hallway.

A State Department spokesman said that Derwinski, a former representative from Illinois, was in Tokyo and "broke off the trip to return home as quickly as possible" when informed of the shooting.

Shultz, who was reportedly on the telephone to Israeli Prime Minister Shimon Peres about the time of the incident, did not hear the gunfire, but was kept informed of the incident while continuing to work, a source said.

Shultz's suite of offices is guarded by a uniformed officer from the Federal Protective Service who screens visitors before they are allowed inside. The suite is also cordoned off from the main hallway by a locked glass door, and visitors must pass through another maze of security screens before entering the secretary's office.

According to a State Department spokesman, Doster joined the department in 1969 as a secretary in the former Bureau of Educational and Cultural Affairs. She also worked in the department's bureaus of administration, intelligence and research and international organization affairs before joining Derwinski's staff last September.

A police source said that Carole Doster and her former husband, whose name was not released, were divorced when their son was a small child. The source said that her son had been unemployed since March, and that previously he had worked as a horse trainer at a local race track.

The letter she sent to the department requesting the revocation of her son's dependent's pass "said that he had threatened her physically," one police source said.

Carole Doster filed a complaint that her son assaulted her on May 27, 28 and 29, according to authorities in Alexandria. He was charged with assault and battery. He was released on personal recognizance and on $500 bond, and was scheduled to appear in Juvenile and Domestic Relations Court in Alexandria on June 26.

After her son assaulted her, Carole Doster went to live for two weeks at the Alexandria Battered Women's Shelter, according to Ellen G. Gilchrist, coordinator of the shelter. She said that Doster showed signs of physical abuse when she arrived at the shelter May 30 and had been to a doctor for treatment of her injuries.

Doster had no contact with her son during her stay, Gilchrist said, and continued to go to work at the State Department because "she felt that going to work she would be safe."

She left the shelter June 15 after having the locks changed on her apartment at the Southern Towers and getting an unlisted phone number, Gilchrist said.

"She felt very secure that the problem with [her son] and the security in her building had been resolved," Gilchrist said. "She felt very confident that she was safe at home."

According to Beth Kersey, property manager at the Southern Towers apartments, where Carole Doster lived, "She had requested a week and a half ago for us not to allow him [her son] to enter her apartment . . . . She said under no circumstances were we ever to give him a key to enter her apartment."

Kersey said that Carole Doster had moved into the apartment six months ago and that there is no record of her son having lived there.

Despite assurances that Shultz was never in any danger, one official at the General Services Administration, which has responsibility for guarding the building through the Federal Protective Service, said, "We were really concerned about this breach in GSA security."

"A gun got in there, so apparently there was a breakdown [in security] somewhere," said Deputy Chief Gibson.

Another police official, who asked not to be quoted by name, said, "You would think that with all the international unrest, security measures would be stepped up, tight as a drum. Apparently it's not."

Security precautions at government buildings throughout the Washington area have been increased markedly over the past two years in the wake of terrorist attacks here and abroad, especially in the Middle East. Concrete barriers were placed at the White House, Capitol Building and other government offices after the 1983 suicide-truck bombing at U.S. Marine headquarters in Beirut and a terrorist bombing of the Capitol a month later.