Section 1115. Officer not to hold any other civil office

Any person holding
  office,  whether  by  election  or  appointment,  who shall, during such
  person's term of office, accept, hold or retain any other  civil  office
  of  honor, trust or emolument under the government of the United States,
  except commissioners for the taking of bail, or of the state, except the
  office of notary public or commissioner  of  deeds  or  officer  of  the
  national  guard,  or who shall hold or accept any other office connected
  with the government of the city, or who  shall  accept  a  seat  in  the
  legislature,  shall be deemed thereby to have vacated any office held by
  such person under the city government; except that the mayor may accept,
  or may in writing authorize any other person holding office to accept, a
  specified  civil  office  in  respect  to  which  no  salary  or   other
  compensation  is  provided.  No  person  shall  hold  two city or county
  offices, except as expressly provided in this charter or by statute; nor
  shall any officer under the city government hold  or  retain  an  office
  under a county government, except when such officer holds such office ex
  officio  by  virtue of an act of the legislature, and in such case shall
  draw no salary for such ex officio; provided, however, that  any  member
  of the police force or any member of the fire department may hold office
  as  a  member of a board of education outside of the city of New York if
  otherwise qualified to serve thereon.