Can my boyfriend sign our child's birth certificate if he is married to someone else?

I am currently 4 months pregnant and my boyfriend is still married to his ex. She is in another country and we have no way of contacting her. We are looking into options for him to get a divorce but it seems nearly impossible to do so before our child is born. I am concerned that there might be any complications with him being able to sign our child's birth certificate when he is born. Can he sign the birth certificate even if he is still married when our child is born.