The Chief Administrator of the Courts, following consultation with and agreement of the Presiding Justice of the First Judicial Department, may establish, by administrative order, a Criminal Division of Supreme Court in Bronx County and assign one or more justices to preside therein. Subject to the further limitations prescribed in this part, such criminal division shall be devoted to the hearing and determination of all criminal cases commenced in or transferred to the courts sitting in Bronx County provided at least one felony or misdemeanor is charged.