Legal Question in Family Law in Michigan

The mother decides whose name goes on the child's birth certificate - and also the child's name. If there is a dispute, it must be handled through the courts, such as by the father commencing an action to determine paternity (verify whether or not the child is his, and thereby reflecting that on the birth certificate). A mother can also choose to list nobody on a child's birth certificate.

The law does presume that the child is that of a woman's husband unless stated otherwise (this is an old fashioned law and has never been updated) - but that doesn't mean much anymore. For example, if the mother died during childbirth and was therefore unable to tell the hospital what to put on the birth certificate, they would automatically put her husband as the child's father, as that's what they're required to do (unless the husband and the father both agreed and told the hospital otherwise) - or the hospital would contact her husband, since they would assume he's the father, etc., and turn over custody of the child to the husband.

If your girlfriend knows you are the father, then she should instruct the hospital accordingly. If her husband has any objections, then paternity testing will have to be performed, and legal action may be necessary.