Crozier spent his junior career with the St. Catharines Teepees of the Junior Ontario Hockey Association (OHA-Jr.) from 1959 to 1962. At the time, the Teepees were sponsored by the Chicago Black Hawks of the National Hockey League. The sponsorship system gave the Black Hawks the rights to all of the Teepees' players. In 1959–60, Crozier helped the Teepees win the Memorial Cup. During his time with the Teepees, Crozier developed his first ulcer, a problem that would plague him for the rest of his career.