New York State’s Education Department has threatened to shut down a for-profit college owned by the Career Education Corporation if the institution — a Katharine Gibbs School in New York City — did not correct faculty and teaching deficiencies, The New York Times reported this morning. The school, a two-year institution that teaches a range of professional skills, is among 13 campuses that Career Education announced last fall that it planned to sell. The state’s action this week could complicate that plan. The Education Department’s move against the college followed a decision last spring by the state’s Board of Regents to impose tougher restrictions and greater oversight of for-profit colleges in the state.