Waxan ku soo koobayaa faqraddan 24ka Juun, 2001-da, oo ku taal NHL Entry Draft
, Connolly iyo Taylor Pyatt waxaa laga iibiyay kooxda Buffalo Sabres si ay u helaan kabtanka kooxda Michael Peca. Ka dib markii uu ka maqnaa kaliya seddex kulan oo xilli ciyaareed caadi ah guud ahaan afartii xilli ciyaareed ee ugu horreeyay horyaalka, dhaawacyadu waxay bilaabeen inay dhibaateeyaan xirfadda Connolly oo bilaabatay 2003-04. Waxa uu ka maqnaa xilli ciyaareedkii oo dhan isagoo qaba cudurka loo yaqaan 'post-concussion syndrome' ka dib markii uu ka soo gaaray dhaawac maskaxeed ciyaartii xilli ciyaareedka ka hor ee ka dhanka ahayd Chicago Blackhawks. Intii lagu guda jiray xiritaanka 2004/05 ee NHL, wuxuu ciyaaray qeybtii labaad ee xilli ciyaareedka SC Langnau ee horyaalka qaranka Switzerland.