The body of Emma, 49, who played for the Blue Devils from 1980-83, was found on a second-floor landing of the building.
Police said the incident has been ruled an apparent suicide.
Unnamed friends told the New York Post Emma had been coping with unspecified health issues recently.
"The Duke basketball family is deeply saddened to hear of the tragic passing of Tom Emma," Duke head Coach Mike Krzyzewski said. "He was a good man and fine representative of Duke University. Our hearts go out to his family and friends. He will be missed."
Emma averaged 7.1 points per game as a guard in 110 career contests for Duke, scoring a career-high 19 points on Nov. 29, 1980, Krzyzewski's first game as the program's head coach.
Emma was president of an athletic training company, Power Performance Inc., at the time of his death.