[2] Following high school, Menefee attended North Texas State Teachers College, where he joined the Eagles men's basketball team as a walk-on.

[4] During his playing career, Menefee, a forward,[2] was a two-time team captain and earned All-American honors in 1943.

[4] While studying at North Texas, Menefee met and married Dorothy Winford, a fellow student.

[2] During his three-month stint on the island, Menefee lost 40 pounds (18 kg) and was wounded by shrapnel, earning him a Purple Heart.

[5] Following his military service, Menefee joined the coaching staff of the Bears men's basketball program at Baylor University.

[2] As athletic director, Menefee oversaw the Baylor Bears football program win a conference championship and participate in five bowl games.

[2] Menefee also established an athletic scholarship program and participated in fundraising for the construction of the North End Zone Complex at Floyd Casey Stadium.

[1] Following his death, he bequeathed a gift to the North Texas Mean Green women's basketball program, as he had developed an interest in the sport following his retirement.