He attended high school in Glenbeulah, Wisconsin before attending the University of Wisconsin-Oshkosh and Northwestern University.
Crosby's grandfather, James Little, was also a member of the Assembly.
In June 1901, Crosby married Rosa M.
Additionally, he was a member of the Clark County, Wisconsin Board, District Attorney of Clark County and a judge on the Wisconsin Circuit Court.
He was succeeded by William Lyman Smith.