That’s a frustrating situation. Yes, normally in order to get a passport for your child you must get the other parent to agree. If you are unable to locate your child’s other parent, you have to petition the court and get a court order in order to get the passport.
However, if you have sole legal custody of your child, you will not need the other parent’s signature in order to obtain the passport. Sole legal custody to one parent is not awarded very often – usually, both parents have joint legal custody. “Legal custody” refers to the right to make long-term decisions about a child, including the child’s education, medical care, and religion. In order for only one parent to receive sole legal custody, normally it must be shown that the other parent is unfit, is absent, or is incapable of making decisions about a child’s upbringing.
If you have joint legal custody over your child, and you cannot find your child’s other parent, you will have to petition the court for an order that waives the signature requirement. If you do know where the parent is but he refuses to sign, you will have to petition the court to require him to sign.