Garrett Park moved sedately toward the fore of the national antinuclear weapons movement last week as most citizens speaking at a public forum said they favored a May 3 referendum proposal to make the tiny Montgomery town a nuclear-free zone.

The referendum proposal states that "no nuclear weapon shall be produced, transported, stored, processed, disposed of nor used" within the town's 123 acres. If the resolution passes next week, Garrett Park possibly will become the first American jurisdiction to outlaw nuclear weapons.

In March, the Town Council unanimously adopted a motion to place the question on the ballot and also adopted a resolution endorsing a nuclear weapons freeze.

The unusual action has focused national attention on the somewhat surprised residents of this tranquil, tree-shaded community.

Without so much as a single picket sign, banner or slogan, about 75 people attended an orderly, congenial forum held by the town's civic association. Before discussion on the proposal began, neighbors listened politely to campaign pitches from candidates for mayoral and Town Council seats, which also will be filled in the May 3 balloting.

Elderly men in suits with felt hats perched on their knees, restless children, women with knitting and white-collar professionals crowded the wooden pews in the restored town hall ablaze with the lights of a television film crew. Most of the citizens appeared to assume the referendum resolution would pass overwhelmingly. Rather than debate whether to support it, people focused discussion on the possible impact of the town's declaration of independence from U.S. military policy and where to go from here. One difficulty has been how to persuade outsiders to take the referendum seriously.

"The problem that bothers all of us is that the whole concept (of nuclear war) is so nebulous that we don't grab at it. How do you make this thing real? When I tell people what Garrett Park has done, they sort of laugh," said Hans Wegner, a researcher at the National Geographic Society.

"We know what the consequences (of a nuclear war) are," said another Garrett Park resident. "But we laugh because we've lost the sense that we can do anything about it. We've become a different kind of country than we were when New England town meetings ran the country."

Robert M. Segal, a management consultant, was one of only two who voiced reservations about the referendum proposal. Though he believes in a nuclear weapons freeze, he said, he does not believe in unilateral disarmament. Declaring Garrett Park a nuclear-free zone is like supporting a drug abuse program but refusing to let a treatment center open up next door, he said.

"Unless you believe in unilateral disarmament, where are these nuclear weapons going to be? In Utah, where they don't want them either? What else are you proposing besides talk?" he asked.

Doug Mitchell, who works for the Congressional Research Service, shared Segal's doubts.

" The referendum does not seem wholly relevant because it doesn't seem likely nuclear weapons would be introduced in Garrett Park. . . . I, at present, would not vote for this referendum item, but if it would be followed up I would certainly be more enthusiastic about it." He suggested that communities like Garrett Park try to establish links with "sister communities" in the Soviet Union through friends, relatives and professional contacts.

Eugene C. McDowell, vice president of the civic association that proposed the referendum to the Town Council in March, warned against "expecting too much of this political gesture and expecting it to be a solution." McDowell was inspired by towns in England near planned nuclear weapons deployment sites that outlawed such weapons within their bounds.

He compared nuclear-free zones to wounds in an organism. "They are pains in the body," he said, "saying 'Look, it hurts here.' The symptom is not part of the solution and no number of nuclear-free zones would solve the problem." The function of nuclear-free zones, he said, would be to "so pain the world organism that it will be compelled to find a way to heal itself before it dies."

The citizens' remarks followed a talk about the effects of nuclear war by Nancy Ramsey, an official of the Committee for National Security, a national group that encourages public debate on arms control and international affairs. She believes the Reagan administration's foreign policy easily could lead to nuclear holocaust, by accident if not by design.