(a) Each criminal case then pending or thereafter commenced in the Supreme Court in such county, and each criminal case thereafter transferred to Supreme Court in such county from Supreme Court in another county, shall be referred for disposition to such criminal division and further proceedings in such case shall be conducted in a part established therein.

(b) All criminal cases then pending or thereafter commenced in the Criminal Court of the City of New York in Bronx County, in which at least one felony or misdemeanor is charged, shall, following arraignment, be transferred therefrom by the Administrative Judge for the Supreme Court in Bronx County to the Supreme Court in such county upon a finding that transfer of these cases would promote the administration of justice, and thereupon such cases shall be referred for disposition to such criminal division and farther proceedings in such cases shall be conducted in the parts established therein. Provided, however, that no criminal case may be transferred pursuant to this subdivision where such case is returnable in a summons part of the Criminal Court and no felonies or class A misdemeanors are charged therein