Yep! Most states do this.However, even today’s Hawaiian state law provides for the issuance of “birth certificates” if the child is born out of state, and potentially out of the US, as long as the legal parents can show Hawaii as their legal residence:
[§338-17.8] Certificates for children born out of State.
How do you think children born overseas and adopted by Americans get a birth certificate in English?
Oh and the birth certificates of these children do NOT say they were born in Hawaii.