RICHMOND, OCT. 9 -- Civil liberties lawyers asked a federal court here today to declare Virginia's appointed school boards unconstitutional, saying they discriminate against blacks.

Virginia is the only state that bans elected school boards, although several states allow localities to opt for apppointed boards, according to Chan Kendrick, Virginia director of the American Civil Liberties Union, which brought the class action lawsuit.

The action, brought in the names of eight blacks who live in various parts of the state, asks the U.S. District Court to require the State Board of Elections and the various local officials who appoint the school boards to come up with plans for the election of members.

The court document traces the history of appointed school boards in Virginia and contends that elected boards were outlawed to prevent blacks from being elected. It adds that the appointive system has resulted in an underrepresentation of blacks.

In Northern Virginia, black appointees constitute three of seven members of the Alexandria School Board, one of five members in Arlington, one of seven in Prince William and one of 10 in Fairfax.

Since Reconstruction, the only Virginia jurisdiction to elect its school board members was Arlington County, which did so from 1947 to 1956, when the option was outlawed by the General Assembly as part of the state's Massive Resistance to federal orders to integrate its public schools.

The ACLU contends that the 1956 ban was passed "for the purpose of . . . continuing discrimination against blacks by assuring white control over school board selection."

Since then, Arlington legislators, joined by some others in recent years, have sought to change the law. The latest effort, led by Del. David G. Brickley (D-Prince William), was killed on a 15-to-5 vote in February by the House Privileges and Elections Committee.

Legislative support for elected school boards has grown over the years. In 1976, Brickley garnered four cosponsors; this year he had 39.

The idea also has the support of the Virginia Education Association, the Virginia Congress of Parents and Teachers, and the AFL-CIO.

The issue has been framed in one of the most hotly contested races for the legislature this fall.

In Henrico County, Republican Senate challenger Eddy Dalton supports elected boards, saying they would give parents a more direct voice in school affairs; Democratic Sen. William F. Parkerson Jr. says elected school boards are meaningless unless they also have the power to tax.

Three methods are employed to select members for the 136 local school boards in Virginia: the members of 47 are named by county boards of supervisors; members of 45 are selected by a commission appointed by a Circuit Court judge; members of 41 are named by town or city councils, and members of three are named by a combination of supervisors and council members.

The ACLU complaint said that requiring localities to appoint school board members, and then failing to appoint blacks in significant numbers, deprives blacks of their rights under the 1st, 13th, 14th and 15th amendments to the Constitution and the Voting Rights Act of 1965.

No date has been set for a hearing.