A 45-year-old official of the U.S. Environmental Protection Agency was fatally stabbed during an apparent robbery last night as she was leaving her office in Crystal City, Arlington County police reported. A 16-year-old youth was taken into custody at the scene.

The victim, Linda M. Billings, was the director of the farm worker safety staff in EPA's office of pesticide programs, according to an EPA official.

Billings, who was described by EPA officials as highly dedicated and given to working long hours, was stabbed several times about 6:40 p.m. on the 11th floor of the building at 1921 Jefferson Davis Hwy., where her office was located, according to authorities.

According to a source familiar with the investigation, Billings managed to get on an elevator and descend to the lobby. When the doors opened, she staggered off and collapsed.

She was found by a guard and taken to the National Orthopaedic and Rehabilitation Hospital, where she died at 9:17 p.m.

Meanwhile, authorities said, the building was sealed and searched floor by floor.

During the search, the source said, the 16-year-old was found in a women's restroom on the ground floor. He was taken into custody by Arlington police, but as of late last night no charges had been placed.

According to the source, a weapon was recovered, but details were not available. There was no immediate indication of what, if anything, was taken from Billings.

An EPA official who did not wish to be identified called Billings "a very hard and dedicated worker . . . very dedicated to the issue of protecting farm workers."

In recent days, the official said, Billings, a GS-15, was deeply involved in the framing of regulations regarding the protection of farm workers from pesticides.

She also was responsible for integrating activities in the pesticide office whenever they involved farm worker protection, the official said.

Billings joined the EPA several years ago. She had served during the late 1970s as a lobbyist here for the Sierra Club, a conservation group.

In 1976 she was quoted in a national magazine in a discussion of the effects of the environmental movement on the nation's economy.

"Environmental laws aren't undermining the national economy," Billings told the US News & World Report. "Cancer caused by pollution is. This one disease costs this country $11 billion a year. Now you tell me what's undermining what."

A neighbor in the Cabin John area where Billings had lived for some time described her as a pleasant woman who enjoyed jogging, kept her lawn trimmed and was involved in civic activities.

The building in which the killing occurred is known as Crystal Mall 2. Security there has been provided in the past several months by Echelon Security Service, a private company based in Baltimore.

Employes with government identification have 24-hour access to the building, according to an Echelon supervisor. He said others must sign in with a guard in the lobby.

The supervisor said only a few people were at work in the building when the stabbing occurred. Two guards were assigned to the building at the time, he said.