Claude Crenshaw was born on December 12, 1918, in Columbia, Louisiana. He enlisted in the U.S. Army Air Forces on February 12, 1942, and was trained as an Aircraft Mechanic at Keesler Army Airfield, Mississippi, before entering the Aviation Cadet Program in January 1943. Crenshaw was commissioned a 2d Lt and awarded his pilot wings on October 1, 1943, and after completing fighter transition training, was assigned to the 369th Fighter Squadron of the 359th Fighter Group in England in April 1944. Lt Crenshaw was credited with the destruction of 7 enemy aircraft in aerial combat, 1 probable, and 3 on the ground while strafing enemy airfields, before returning to the U.S. in December 1944. After the war ended, he served as an Air Intelligence Staff Officer before leaving active duty and going into the Air Force Reserve on February 2, 1950. Capt Crenshaw returned to active duty on July 1, 1953, and after completing refresher pilot training and jet transition training, he served as a flight instructor with the 3566th Pilot Training Squadron at James Connally AFB, Texas, from November 1953 to March 1954. His next assignment was as a gunnery instructor at Nellis AFB, Nevada, from April 1954 to April 1955, followed by service on the staff of Headquarters 12th Air Force at Weisbaden AB, West Germany, from August 1955 to June 1958. Maj Crenshaw next flew F-100 Super Sabres and served as an Operations Staff Officer with the 479th Tactical Fighter Wing (TFW) at George AFB, California, from June to October 1958, and then as an Operations Officer with the 436th Tactical Fighter Squadron (TFS) at George from October 1958 to June 1959. His next assignment was as Executive Officer and then Commander of the 435th TFS at George from June 1959 to July 1960, followed by service as Commander of the 436th TFS at George from July 1960 to September 1961. During this time, he deployed with the squadron to Moron AB, Spain, from August to December 1960. Col Crenshaw served as Wing Plans Officer for the 479th TFW from September 1961 to January 1962, and then served as Commander of the 434th TFS from January to June 1962. He next served as Commander and then Operations Officer with the 4443rd Combat Crew Training Squadron at George AFB from July 1962 to July 1964, and then deployed with the squadron to Athens, Greece, from February to September 1964. He served on the staff of the 479th TFW at George from September 1964 to January 1965, and then served with the 436th TFS at George from January 1965 until his retirement from the Air Force on August 1, 1965. Claude Crenshaw died on March 17, 1972, and was buried at the Victor Valley Memorial Park Cemetery in Victorville, California.

His Distinguished Service Cross Citation reads:

For extraordinary heroism in action against the enemy while serving as flight leader in a bomber support mission in the vicinity of Merseburg, Germany, 21 November 1944. On this date, accompanied by only his wingman, Captain Crenshaw attacked a formation of one hundred enemy fighters having a top cover of thirty five additional fighter aircraft. In his great desire to protect the bomber formation, he pursued the enemy relentlessly, destroying four of their aircraft and damaging still another despite the enemy's vast numerical superiority. The outstanding heroism and determination to destroy the enemy displayed by Captain Crenshaw on this occasion are in keeping with the highest traditions of the Armed Forces of the United States.