Crossin was already a ballyhooed player during his high school days; in 1941 he led all Pennsylvania schoolboys in scoring. He was then the Quakers' leading scorer his first two seasons, scoring 237 points in 21 games in 1943 and 190 in only 14 games in 1944. On January 26, 1944, Crossin dropped 29 points in a 53-45 win over Swarthmore to break the school's single-game scoring record that had been set 23 years earlier by Danny McNichol. At the end of the 1944 season, he was named second-team All-America by Pic Magazine. (Pic's first team had a couple of notable names that year-George Mikan of DePaul, and Otto Graham of Northwestern.)
The Quakers' captain for both the 1943-44 and 1946-47 seasons, Crossin was a two-time recipient of the program's Arthur Kiefaber MVP Award, in 1943 and 1947. In 1944 and 1947, he was honored with the program's Bus McDonald Award as the Most Inspirational Player.
Following his Penn playing career, Crossin was the first-round pick of the Philadelphia Warriors in the 1947 Basketball Association of America (BAA) draft and played three years for the franchise. Prior to his third and final season, the BAA would change its name to one more familiar to today's basketball fan-the National Basketball Association, or NBA.
Crossin also played in the American Basketball League (ABL) for the Wilkes-Barre Barons, and coached the ABL franchise in Allentown in the early 1950s. Following that, he served in the state House of Representatives and was a Luzerne County Commissioner. Crossin also spent a number of years as a college basketball official in the ECAC.