ยง  4133.  Birth  certificate;  incomplete;  duty of registrar. 1. If a
  certificate of birth is incomplete, the registrar  of  the  district  in
  which  the  birth  occurred and with whom the certificate has been filed
  shall immediately notify the person who signed the record,  and  require
  him to supply the missing items of information if they can be obtained.
2. In any case where the physician or nurse-midwife in attendance upon
  the  birth  of  a  child  within this state, or other person reporting a
  birth of a child within this state as provided by section four  thousand
  one  hundred  thirty of this chapter, is unable, by diligent inquiry, to
  obtain any item or items of information required  in  this  article,  it
  shall  then  be  the  duty of the registrar to secure from the person so
  reporting, or from any other person having the required knowledge,  such
  information  as  will enable the registrar to prepare the certificate of
  birth herein required.
3. It shall be the duty of the person reporting such birth or  who  is
  interrogated  in relation thereto to answer correctly and to the best of
  his knowledge all questions put to him by the  registrar  which  may  be
  calculated to elicit any information needed to make a complete record of
  the  birth  as contemplated by this article, and it shall be the duty of
  the informant as to any statement made in accordance herewith to  verify
  such  statement  by  his  signature,  when  requested  so  to  do by the
  registrar.
Structure New York Laws
Title 3 - Registration of Births
4131 - Births; Registration; Foundlings.
4132 - Birth Certificate; Form and Content.
4133 - Birth Certificate; Incomplete; Duty of Registrar.
4134 - Birth Certificate; Unnamed Child.
4135 - Birth Certificate; Child Born Out of Wedlock.
4135-A - Birth Certificate; Child Born in Prison.
4135-B - Voluntary Acknowledgments of Parentage.
4136 - Birth Certificate; Statement as to Blood Test.
4137 - Births; Notice of Recording.
4138-A - Certificate of Birth Data.
4138-B - Birth Certificate: Foreign Country Adoption.
4138-C - Adoption Information Registry.
4138-D - Mutual Consent Voluntary Adoption Registry.
4138-E - Adoptee's Right to a Certified Copy of His or Her Birth Certificate.