Connolly made his international debut with Hockey Canada, representing Team Pacific at the 2009 World U-17 Hockey Challenge. He helped the team to the gold medal game, where they lost 5–1 to Team Ontario. Connolly recorded eight points (three goals and five assists) over six games. Several months later, he joined Team Canada for the 2009 IIHF World U18 Championships. He scored six points in six games as Canada placed fourth. Connolly remained with the national under-18 team for the Ivan Hlinka Memorial Tournament in August 2009. Connolly recorded an assist in the gold medal game, helping Canada to a 9–2 win over Russia. During the tournament, Connolly hurt his hip, a nagging injury that sidelined him long-term throughout the following season.