During his 45-plus years of practice, Connelly has come to be regarded as one of the leading federal tax litigators in the United States. A shareholder at Chamberlain Hrdlicka in Houston since 1987, he focuses his practice on IRS audit, collection, and criminal matters including civil and criminal tax litigation matters for individuals, companies, and estates.

Outside the courtroom, Connelly has long mentored young lawyers through both his daily interactions and formal presentations, including his involvement on the Student Development Task Force for Earl Carl Institute at the Thurgood Marshall School of Law at Texas Southern University.