In the U.S. this is how you request to check vital records:

https://www.health.ny.gov/health_care/medicaid/publications/...

REQUEST FOR VERIFICATION OF BIRTH

TO WHOM IT MAY CONCERN:
PLEASE PROVIDE BIRTH VERIFICATION THAT A RECORD OF THIS INDIVIDUAL’S BIRTH IS ON FILE TO ALLOW
US TO PROVIDE SERVICES FROM THIS AGENCY.

http://www.dshs.texas.gov/vs/reqproc/verification.shtm

Birth and Death Verifications

Applicants verifying births or deaths will receive a letter stating whether a record of birth or death is on file with the State of Texas. If a record is filed, the verification letter will include the person's name, the date of the event, and the county where the event occurred. Verification letters are available for births or deaths that have occurred since 1903.

Verification letters are not considered legal substitutes for certified copies of birth or death certificates. The Vital Statistics Unit strongly recommends that applicants ensure a verification will satisfy its intended use.