The board of directors of the all-white Salisbury Country Club has rejected for a second time the membership application of a black dentists and his family.

The board's 8-to-7 vote against the family of Dr. Thomas J. Wright followed about a half-hour of discussion on the bid last night.

The vote was well short of the necessary three-quarters favorable tally needed for membership in the club, to which several prominent Virginians belongs.

Last night's aciton was followed today by the resignation from the club of Virginia Attorney General Anthony F. Troy. Troy earlier had objected to the club's exclusion of blacks but said he would continue his membership in an effort to change the policy. He said yesterday that in view of the second board vote he does not believe, as a statewide office holder, that he should remain in the club.

At least two other members reportedly withdrawn from the Chesterfield County country club, incluing a former president of the club, Samuel H. Dibert.

The Wrights first were turned down at the board's June 28 meeting, along with the family of Kanses Cith Chiefs football player Willie Lanier. The Lanier subsequently withdrew their membership application.

Repeating the position he has taken throughout the three-month controversy, club president Thomas J. Hampton said "Salisbury Country Club is a private club. The matter of membership is a private club matter, and we have no further comment.