(a) If a child born in this State is adopted in this State or in another state, the State Registrar shall file a new certificate of birth upon receipt of a certified copy of the decree of adoption from the proper authorities of the state in which the adoption took place.
(b) If the adopted child was born outside this State, and a certificate of birth cannot be secured from the place of birth, the State Registrar may file and issue a special birth certificate as herein provided, upon receipt from the agency responsible for the adoption of evidence of the birth, considered satisfactory by the Registrar.