A splinter group from yesterday's tour of Washington's downtown "fallout shelters" organized by the Women Strike for Peace fetched up in the basement of the Lafayette Building on Vermont Avenue NW in a stuffy hallway three floors below the ground.

Two reporters, a doctor from Physicians for Social Responsibility, an American University student in a wheelchair--he is a multiple sclerosis victim writing a play about people in a fallout shelter--and two representatives of the Women Strike for Peace were in the party. They were being shown around by a pleasant young man named Michael Penn, the acting building manager.

One of the peace strikers, Gladys Thomas, a white-haired woman with a penetrating voice, called out, "There's no air in here. What about carbon monoxide?"

Penn explained, not for the first time, that he was not really showing us a fallout shelter, "just a designated area and facility below ground."

The two engineers who maintain the building's heating and air conditioning looked blank when asked about cots, food supplies, flashlights, radiation monitors and other amenities of civil defense.

"We had some old Army cots," one of them said vaguely, "but they moved them out a while back."

Penn said, "We deal with conventional-type disasters, fires and bomb threats and things like that.

He was asked who would be in charge in the event of a nuclear attack.

"I don't know who is in charge of getting people down here," he said. "It just hasn't come up."

He offered the name of Alvin Turner of the buildings protection section of the Government Services Administration.

Turner, when reached by telephone, said he is involved with guards and the cleaning of government buildings.

"We have certain procedures to protect the buildings, but we are talking about facilities, not people," he said. Perhaps FEMA (Federal Emergency Management Agency, which has taken over civil defense) could help.

James Holton, public affairs director of FEMA, said, "This is going to sound like a cop-out, but the shelters are the responsibility of the local government. The federal government in the mid '60s decided that the whole idea of maintaining bomb shelters was no longer a sensible idea in urban areas.

"One of the first things that it did was to advise the states to get rid of all that stuff, the crackers and things. The new idea is crisis relocation planning, to take people out into areas where they would have a better chance of survival," he said.

The local official responsible for the safety of Washington residents is Richard G. Bottorff, acting director of the D.C. Office of Emergency Preparedness, who said there are plans to train shelter managers to make the tough decisions about whether to admit irradiated people into underground facilities such as the Lafayette Building.

Bottorff and his city government colleagues would head for a protected site at the Lorton Correctional Center in Fairfax County. The contract has been signed.

For Washingtonians who might be caught by surprise at ground zero, there are 7,000 large buildings, all of which, except for foreign embassies and consulates, would be open to the public. Bottorff thinks that if the bomb came, they would open their doors to the locals.

The current facilities have been "destocked" of emergency supplies, and no restocking is in progress. Nor has the D.C. government made any arrangements with "host areas" in Virginia and West Virginia.

"We are not authorized to contact them," Bottorff said. "The federal officials want us to wait for another year or 18 months before we do anything."

The Women Strike for Peace delegation came up out of the bowels of the Lafayette Building and into the day's gray light. Penn said somberly, "If it comes, hopefully I would be incinerated in the first five minutes."

The scruffy column, about 60 strong, mostly gray-haired women in comfortable shoes and with a sprinkling of children, reformed and trudged to Lafayette Park, chanting, at the exhortation of their marshals, "One-two-three-four, we don't want a nuclear war" and "Two-four-six-eight, we don't want to radiate."

A two-man motorcycle escort held the lunchtime traffic for them at intersections. Passersby eyed them warily. The hustling lawyers from K Street, the smug bureaucrats on I Street seemed to flinch at the sounds of old anti-Vietnam songs updated. Richard Nixon made the important discovery that some Americans would rather see a war than a demonstration. President Reagan is counting on the cry of "unilateral disarmament" to repel the legions clamoring for a nuclear freeze.

Outside the Army & Navy Club, a gray-haired man refused a leaflet saying, "You should be demonstrating in Moscow, too."

In the park, the doctor, Ralph Yodaikin, who took annual leave from his job at the Department of Health and Human Services to make the tour, called FEMA's civil defense preparations "one large adult pacifier aimed at stopping us yelling against this whole nuclear holocaust we see coming over the horizon."