Born in Buffalo, New York, Crotty received a Bachelor of Arts degree from the University of Notre Dame in 1962 and a Bachelor of Laws from Cornell Law School in 1967.
Crotty entered private practice in New York City at the prominent law firm of Donovan, Leisure, Newton & Irvine, working there as an associate from 1969 to 1976, and then as a partner from 1976 to 1984, and from 1988 to 1993.
From 1984 to 1988, he held several government positions in the Office of Financial Services for the City of New York.
After having returned to private practice for a time, he became the Corporation Counsel from 1994 to 1997, and group president for the New York and Connecticut region for Verizon Communications from 1997 to 2005.
On February 14, 2005, Crotty was nominated by President George W. Bush to a seat on the United States District Court for the Southern District of New York vacated by Harold Baer Jr. Crotty was confirmed by the United States Senate on April 11, 2005, and received his commission on April 15, 2005.