The D.C. Board of Elections and Ethics yesterday formally placed on the Nov. 2 ballot an initiative that would compel city officials to support a bilateral freeze on nuclear weapons.

The board also ruled that Republican mayoral candidate E. Brooke Lee is a legal resident of the District and that his name is to remain on the Sept. 14 primary ballot. The board's action dismissed an effort by James E. Champagne, Lee's opponent, to remove him from the ballot on the basis that Lee did not meet the city's residency requirements.

In other action, the board gave two groups permission to begin petition drives to place two additional initiatives on the ballot in 1983. These include an initiative that the city support the preservation of the historic Rhodes Tavern at 15th and F streets NW, and another initiative that would sharply reduce the salaries of school board members.

Supporters of the nuclear freeze initiative, the D.C. Campaign for a Nuclear Weapons Freeze, needed a total of 13,181 signatures to qualify for the ballot, including at least 5 percent of the registered voters in five of the city's eight wards. The group turned in 23,529 signatures.

Champagne said he would no longer contest Lee's right to remain on the ballot although under city law he could appeal the board's ruling. "I just wanted to get the issue to the public," Champagne said. The board took less than five minutes to reach its decision after hearing about 40 minutes of testimony.

Champagne had contended that Lee had not met the legal requirement of living in the District one year before the scheduled Nov. 2 election.

The committee seeking an initiative on the Rhodes Tavern issue has been locked in a four-year battle with developer Oliver Carr over the preservation of the District's oldest remaining commercial building in downtown.

Carr has won the legal right to demolish or move the building, but has not said what he plans to do.

The school board initiative, sought by a group of citizens that includes former school board president Minnie S. Woodson, would limit school board salaries to about $7,000, about one-third of what the members are now paid. Woodson said that lower salaries would attract persons who are more civic minded than interested in launching political careers.