Nancy was one of four children born to Stephen and Ruth Phillips Batson of Birmingham. She attended public schools in Birmingham and then entered the University of Alabama. She was elected president of her residence hall as a junior and president of the Women's Student Government Association as a senior.
In 1939 Crews was one of five women at the University selected for civilian flight training. She earned her private pilot's license in 1940 and her commercial license in 1942. That fall she became one of the original 28 members of the Women's Auxiliary Ferrying Squadron that performed stateside missions during World War II. She shuttled P-38, P-47 and P-51 aircraft between their factories, staging areas, maintenance sites and training sites.
After the war all female pilots were discharged and she returned home, married Paul Crews, and raised three children in California City, California. In the late 1950s she returned to flying, buying a Mooney Mite airplane and competing in Powder Puff Derbies. She worked as a glider instructor and eventually opened her own flight service in California. After her husband's death in 1978 she served one term as California City's mayor.
Crews later returned to Birmingham and developed single-family houses on land she inherited from her father. She served one term as commissioner of the St Clair County Airport and became the first female inducted into the Alabama Aviation Hall of Fame in 1989. She was inducted into the Alabama Women's Hall of Fame in 2000.
Crews organized a 1999 reunion of WAFS veterans that led to Sarah Rickman's 2001 book about the original members of the flying service. After her death that year, Rickman, who publishes a newsletter for surviving World War II female aviators, began writing Crews' full-fledged biography. Crews' WAFS flight suit and logbook, as well as her Mooney Mite, are in the collection of the Southern Museum of Flight.
When the members of the WAFS and its successor, the Women's Airforce Service Pilots (WASP) received the Congressional Medal of Honor in 2010, Crews' family designated her biographer to accept the award on her behalf.