[2] Undrafted, Connolly, like his brother, opted to pursue a professional career abroad and signed to play the 2012–13 season, with Swedish team Färjestad BK in Elitserien.

After two seasons, Connolly left as a free agent to sign with fellow SHL club, Leksands IF on April 23, 2014.

In the 2014–15 season, Connolly left Leksands after 8 scoreless games to join HockeyAllsvenskan club, Rögle BK on October 9, 2014.

Connolly adapted quickly to produce 30 points in 40 games to help Rögle BK gain promotion to return to the SHL.

His father-in-law is Jamie Stauber, a member of a well-known hockey playing family from Duluth, Minnesota.