Since both you and your child's father have legal rights to parent the child, most states require the signature of both parents in order to put a child up for adoption. You may be wondering if this means that your baby's father can step in at the last minute and stop you from putting the child up for adoption. In some situations, he may be able to do just that. Here's a look at what you need to know about how your child's father can influence the adoption process.