Connelly qualified as a Chartered Physiotherapist in 1993 and began his football career at his local side Hallam before Stockport County manager Danny Bergara offered him a professional contract at the club, one that he accepted on finishing his degree in physiotherapy. He helped Stockport to the semi-finals of the 1996-97 League Cup, beating Premier League teams Blackburn Rovers, West Ham United and Southampton en route. In the semi-finals they faced another Premier League team in Middlesbrough. Boro won the first leg 2–0 at Edgeley Park. In the second leg at the Riverside, Connelly gave Stockport an early lead. However they were unable to score again and lost 2–1 in aggregate. His impressive form even generated rumours of a possible move to Liverpool, although this failed to materialise.
