The Columbia University Medical Center is an academic medical center affiliated to the Columbia University.
Following the Clash of the Avengers, James Rhodes was seriously injured by Vision's blast. Requesting for medical assistance, Tony Stark brought Rhodes to the Columbia University Medical Center for treatment. While Rhodes was X-Rayed, Stark questioned how Vision could make a mistake like that and Vision admitted he had been distracted by Wanda Maximoff, which neither he nor Stark had known could happen.
Outside of the operating room, Stark was approached by Natasha Romanoff. He then explained her Rhodes' condition before saying how disappointed he was as she allowed Steve Rogers and Bucky Barnes to escape, inadvertently leading to Rhodes' accident. Although Romanoff insisted that they had made all of the wrong actions in trying to resolve their situation, Stark then called her a double agent for assisting Rogers.
Stark informed Romanoff that T'Challa had reported Thaddeus Ross about her betrayal and that the Joint Counter Terrorist Centre was going to arrest her. Romanoff insisted they went about this wrong, as Stark commented that betraying people was something Romanoff seemed unable to help. He made no attempt to help or detain her as she left the Center to go underground.