He played for the University of Wisconsin from 1974 to 1977 where he was an All-American twice (1976 & 1977) and helped the team win the 1977 NCAA championship. The Montreal Canadiens chose him 173rd overall in the 1975 NHL Amateur Draft while the Houston Aeros selected him 213th overall in the 1974 WHA Amateur Draft. In the NHL he played in 104 games and scored 17 goals and 58 assists. Norwich played for the United States in the 1977 and 1981 World Championships.