No, it’s not mandatory to have a birth certificate. However, birth records are public records, and any researcher can search the registers.
About Vital Records Vital records (birth, death, marriage, and divorce certificates) for events that occurred in Hawaii are received and preserved by the Office of Health Status Monitoring, a unit of the Department of Health. In Hawaii, access to vital records is restricted by statute (HRS §338-18). Certified copies of these records may be issued to authorized individuals and used for such diverse purposes as school entry, passports, Social Security participation, drivers licenses, employment, sports participation, survivors benefits, proof of property rights, and other needs.
Well, since we don’t care if you’re a citizen to vote, this just follows.