Maurice began playing with the Windsor Spitfires of the Ontario Hockey League (OHL) in 1984–85, appearing in 38 games with the club and earning three assists. He was held off the scoresheet in four playoff games, as Windsor was swept by the London Knights in the first round. After his rookie season, Maurice was selected by the Philadelphia Flyers in the 12th round, 252nd overall, in the 1985 NHL Entry Draft, which was the final selection of that year's draft.