2019 New York Laws
DOM - Domestic Relations
Article 3 - Solemnization, Proof and Effect of Marriage
20 - Records to Be Kept by the State Department of Health and the City Clerk of the City of New York.

§  20.  Records  to  be kept by the state department of health and the
  city clerk of the city of New York. All original affidavits, statements,
  consents and licenses with certificates attached, and also  all  written
  contracts  of marriages outside of the city of New York shall be kept on
  file and properly indexed by the state department of  health,  and  such
  similar  evidences  of marriage in the city of New York shall be kept on
  file and properly indexed by the city clerk of the  city  of  New  York.
  They  shall  be  carefully  examined,  and if any such are incomplete or
  unsatisfactory the state commissioner of health and in the city  of  New
  York  the  city  clerk  shall  require  such  further  information to be
  supplied  as  may  be  necessary  to  make  the  record   complete   and
  satisfactory.  Whenever  it  is  claimed  that  a  mistake has been made
  through inadvertence in any  of  the  statements,  affidavits  or  other
  papers required by this section to be filed with the state department of
  health,  and  in  the city of New York with the city clerk's office, the
  state commissioner of health and in the city of New York the city  clerk
  may  file with the same, affidavits upon the part of the person claiming
  to be aggrieved by such mistake, showing the true facts and  the  reason
  for  the mistake and may make a note upon such original paper, statement
  or affidavit showing that a mistake is claimed to have been made and the
  nature thereof.