Harry is playing the doctor (John Cullum/Yves Montand) role, according to PLaybill:
Here's how they bill the show: "Love blooms in unexpected places in the delightfully reimagined world of On a Clear Day You Can See Forever. Still in love with his deceased wife, Dr. Mark Bruckner (Harry Connick, Jr.), a dashing psychiatrist and professor, unknowingly takes on the case of his life with David Gamble, a quirky young florists' assistant.