Birth Certificates can be ordered online. Overview: Vital Records has birth records (since 1881) for all of New York State except New York City.Be careful when you fill out your baby's full name and your mailing address. Correcting a birth certificate can cost money or even require a trip to court. To assist you in determining your eligibility to sign an Acknowledgment of Parentage, the following definitions are provided:. This form is filed with the Court after the service is done. This form is called an Affidavit of Service. You can order a certified short form or long form copy of a birth certificate for someone born in New York City in or after 1910. Application for a certificate can be obtained at the clerk's office of the court where the sentence was given. You don't have to submit them in original.