What country did this occur in? If USA then what state. If the child was born "stillborn" then there may only be a "Certificate of Fetal Death or Still Born Death" issued, no bc as those are officially known as "certificate of Live Birth". If the child was born alive then died then there could be a CLB and and a death certificate issued.
As far I have seen anyone can get a "genealogy" bc or dc. Just the "certified" with a seal used for ID purposes is restricted.