Brandon Carey, the general counsel for Oklahoma City public schools, said that the Douglass case presented a “very unique and different situation.” The school district is not questioning the referees’ judgment in calling a penalty, Mr. Carey said, but seeking redress because the referees did not know the rules about assessing the penalty.

Image The Nov. 28 game between Locust Grove and Douglass. During the game, officials wrongly negated a late Douglass touchdown. Credit... Bryan Terry/THE OKLAHOMAN, via Associated Press

“The ruling negated a touchdown in the final 64 seconds and probably completely changed the outcome,” he said. Referring to a potential replay of the Douglass-Locust Grove game, Mr. Carey added, “Just because it hasn’t been done doesn’t mean it’s not the right thing to do.”

Among supporters of a replay is Barry Switzer, who won three national championships coaching the University of Oklahoma and a Super Bowl title coaching the Dallas Cowboys.

“Let the play on the field determine who won the ballgame,” Mr. Switzer told reporters.

In 1972, a state football semifinal between two Louisiana schools was replayed in its entirety, not for legal reasons but because the score was 0-0, the tiebreakers remained even and there was no provision for overtime.

It has grown increasingly common over the past two decades for courts to address issues of eligibility for high school players and teams in state playoffs. In 2005, a high school quarterback from Oklahoma challenged a two-game suspension for kicking an opponent during a playoff game. Eventually, the Oklahoma Supreme Court upheld the suspension.

While some attempts to replay games have succeeded in lower courts, they have been reversed by appellate courts, said Mr. Goldberger, the sports law expert.

He cited a 1981 case in which the Georgia Supreme Court overturned a lower-court ruling to replay the final seven minutes of a high school football game there because of a referee’s mistake.