The man police shot and killed inside a Brooklyn hospital Thursday evening was a former NYPD officer who had barricaded himself in a room and threatened to kill two people with a broken part of a hospital toilet, authorities said. Michael Lynch, 62, of Fort Greene, Brooklyn, resigned from the NYPD in the 1990s, according to police officials and his family. Police said they did not know why Lynch was at the hospital Thursday and were still investigating the circumstances that led to the confrontation.