Twelve more persons were arrested yesterday in brief skirmishes involving dwindling numbers of antinuclear demonstrators outside the Seabrook nuclear power plant. It brought to 38 the number arrested during three days of protests.

Eight of the latest arrests came as protesters tried once again to cut through a fence around the embattled construction site. Most of those arrested have been charged with trepass and disorderly conduct.

A state trooper said at least 13 protesters were injured during the holiday weekend, none seriously. Leaders of the protesters said at least 60 persons were treated for injuries.

Yesterday's activities bore little resemblance to the determined assaults on the plant's fences Saturday by as many as 1,500 protesters. Estimates of the number of demonstrators dropped to 600 yesterday.

At a news conference, spokesmen for the Coalition for Direct Action at Seabrook, which organized the holiday weekend protest, said they planned a "mass presence and moving picket" along U.S. 1 in front of the plant. They said direct action -- apparently fresh attempts to breach the fences -- would resume later.

Meanwhile, in Manchester about 50 miles to the west, 24 demonstrators were arrested and charged with criminal trepass following a sit-in at the headquarters of Public Service Co. of New Hampshire, the builder of Seabrook. Three demonstrators were treated for minor injuries.