Alexander Hamilton was a prolific writer. He authored 51 of the 85 Federalist Papers, co-authored 3 more, and left many other documents and letters. In all of this, there doesn't seem to be any first-hand statement from Hamilton about religion, only accounts by others as to what he said. His son John Church Hamilton attributes this one to the Reminiscences of General Morton.
"I have carefully examined the evidences of the Christian religion, and if I was sitting as a juror upon its authenticity I would unhesitatingly give my verdict in its favor."
According to the Episcopal minister, Dr. John Mason, Hamilton, on his deathbed said,
"I have a tender reliance on the mercy of the Almighty, through the merits of the Lord Jesus Christ." - Memoirs of John M. Mason