May attended college at Indiana University. May was a power forward on the 1976 Indiana basketball team that went undefeated and won the NCAA championship under coach Bobby Knight. May was named NCAA men's basketball national player of the year in 1976. He won a gold medal as a member of the United States basketball team in the 1976 Summer Olympics. In 1975 Indiana finished the regular season undefeated, but May broke his arm in the final week of the season. In the NCAA tournament regional final against Kentucky, Knight started May in place of John Laskowski, who had played well in place of May. May was rusty and Kentucky upset Indiana, 92-90, to reach the Final Four.
May and his wife, Debbie, have two sons who were members of basketball teams that played in NCAA national championship games. Scott May Jr. was a member of the 2002 Indiana team that lost to Maryland. Sean May helped North Carolina win a national championship in 2005 and currently plays for the NBA's Charlotte Bobcats.
- Scott May scored 26 points in the NCAA Championship Final Four and that feat was also done by his son Sean May in 2005 in the NCAA Championship game against Illinois.