The proceeds from lucrative bingo games sponsored by tax-exempt schools in Virginia cannot be used for educational purposes unless the students who benefit "are needy or legitimate objects of charity," according to an opinion issued by State Attorney General J. Marshall Coleman.

The opinion, which does not have the force of law, casts doubt on the way in which many nonprofit, tax-exempt charitable organization use their bingo profits.

One such group is the Montessori School of Alexandria Inc., which last year used more than $240,000 in profits from bingo games to defray mortgages, purchase land and begin construction planning for a new building. Tuition at the school averages $1,000 according to Dirgham Salahi, the school's director, who said 10 percent of the student body receives some scholarship aid.

State Sen. Wiley F. Mitchell Jr. (R-Alexandria), who requested the opinion, said yesterday that the 1974 state bingo law may now be changed to give schools more fundraising flexibility.

"I did not ask the question of (of Coleman) in an attempt to be critical of any one school, but rather to see if the attorney general agreed with me about the use of money under the law as it now stands. Personally, I think any nonprofit school ought to be able to use the money for its own corporate purposes. The law as it is written is unduly restrictive," Mitchell said.

Coleman's letter, dated Aug. 10, also contains the attorney general's opinion that athletic groups that sponsor bingo games can only use the proceeds to purchase uniforms and equipment "if those who receive the benefit of the proceeds are legitimate objects of charity."

The Montessor School bingo fundraising operation accounts for nearly half of the $1.2 million grossed by Alexandria's bingo games each year.Since the school began sponsoring bingo games in 1974, it has paid off more than one-third of its $155,000 mortgage, purchased 10 acres of land for $112,000 cash, and started planning for the first Montessori high school in the country.

A Circuit Court grand jury indicted Alexandria Commonwealth's Attorney William L. Cowhig on a bribery charge Aug. 3, accusing him of accepting $34,000 in bribes from Salahi, who has not been charged with any criminal offense.

Charles Craven, a parent of a Montessori student who oftens volunteers to conduct the school's bingo games, remarked yesterday: "Without bingo you can forget the high school. The tuition will go up and the enrollment will go down. We couldn't bake enough cakes to pay off our debt. Bingo did it."