The Arlington County Board's sole Republican member, Michael E. Brunner, proposed yesterday that the board change the way it appoints School Board members, saying the current procedure amounts to a "political spoils-type system."

Brunner, a former School Board member, asked the County Board's four Democrats to consider a system similar to Fairfax County's, under which each of Arlington's elected County Board members would designate a School Board appointee. Currently, appointments are ratified by a majority of the five-member County Board, whose members are elected at large.

There were mixed reactions to the proposal yesterday. Members of both the County Board and the School Board said they saw the potential for more political appointments because the nominee might be chosen because of personal friendship or campaign work instead of qualifications. Legally, school appointees are responsible only to the state School Board.

Mary Margaret Whipple, the County Board's Democratic vice chairman and a former School Board member, said she expected the County Board to discuss the proposal. But she gave it little chance of passing, as it has been proposed and rejected before.

Brunner said his plan would bring elected school boards "one step closer." They have been barred in Virginia since 1959, when Arlington's elected School Board voted to desegregate the county's schools.

Noting widespread support for School Board elections and repeated refusal by the General Assembly to approve them, Brunner said citizens would have a more direct role in School Board appointments if they could discuss School Board qualifications with County Board candidates.