Section 600-A. Jail time records and certificates

A record shall be kept by
  the  sheriff,  or  in  counties  within  the  city  of  New  York by the
  commissioner of correction of such city, of all jail time to  which  the
  defendant  is  entitled  under subdivision three of section 70.30 of the
  penal law. In  any  case  where  the  sheriff  or  the  commissioner  of
  correction  of  the  city  of  New  York  has  the  duty of delivering a
  defendant to an institution  not  under  his  jurisdiction  pursuant  to
  sentence   and   commitment,  such  person  shall  deliver  a  certified
  transcript of such record to the person to whom the defendant is  to  be
  delivered.