The Gotham General Hospital is one of the most renowned health care institution of Gotham City. Because of it's importance, many of the most notable residents of Gotham have been patients at the hospital at one point or another.
As any other institution operating in Gotham, the General Hospital has been target of some of criminals, from the lesser crooks, to the most ruthless super-criminals native of the city. At one point, the hospital was attacked by the gang leader "Whale" Morton during his cat-related crimes.
When Selina Kyle was attacked by Hush and he removed her heart, she was taken into the intensive care unit of the hospital; where she was protected by Dr. Midnight and Mr. Terrific. After Batman recovered her heart, both of them performed surgery on her, putting her heart back successfuly and afterwards, Selina was taken to the ICU. Bruce visited Selina while she was recovering and told her that he has always loved her.