2015 New York Laws
PBO - Public Officers
Article 2 - (Public Officers) APPOINTMENT AND QUALIFICATION OF PUBLIC OFFICERS
5 - Holding over after expiration of term.

 5. Holding  over  after  expiration of term.  Every officer except a
  judicial officer, a notary  public,  a  commissioner  of  deeds  and  an
  officer  whose term is fixed by the constitution, having duly entered on
  the duties of his office, shall, unless the office shall terminate or be
  abolished, hold over and continue to discharge the duties of his office,
  after the expiration of the term for which he shall  have  been  chosen,
  until  his  successor  shall  be  chosen  and  qualified;  but after the
  expiration of such term, the office  shall  be  deemed  vacant  for  the
  purpose of choosing his successor. An officer so holding over for one or
  more  entire terms, shall, for the purpose of choosing his successor, be
  regarded as having been newly chosen for such terms. An appointment  for
  a  term  shortened by reason of a predecessor holding over, shall be for
  the residue of the term only.