Could Cuomo face an impeachment inquiry? Impeachment in NY Gov. Andrew Cuomo is dealing with mounting criticism and even calls to resign. But could he be impeached? This is how impeachment works in New York state. NEW YORK - Gov. Andrew Cuomo on Wednesday said he was not going to resign over allegations of sexual harassment even as New York Democrats and Republicans alike have called for him to step down. "I wasn't elected by politicians, I was elected by the people of the state of New York," Cuomo said. But while politicians did not elect him, they do have the power to impeach and remove him.