A letter of consent, preferably in English and notarized, from the other parent or signed by both custodial parents. The letter should say: "I acknowledge that my child is traveling outside the country with the name of the adult with my permission."
The letter should include the other person's contact details and details about the trip. It also helps if you've: evidence of your relationship with the child, for example a birth or adoption certificate. a divorce or marriage certificate, if you are a single parent but your family name is different from the child's.
Your child will need a Child Travel Consent any time they're traveling without all their parents or legal guardians present. If your child is traveling alone, with only one parent, or with a non-legal guardian, they will require a Child Travel Consent signed by both parents or legal guardians.
Unless your specific court order prevents out-of-state travel or other restrictions, generally each parent may choose to travel.
It is not mandatory that you have a signed letter from the other parent, as long as the border officials are satisfied that you have proper approval from that parent, or a court, to travel with the child.
The United States Does Not Have Exit Controls: Two-parent consent is not always needed for a minor to leave the United States. Without a valid court order prohibiting the child's travel outside of the United States, there may be no way to prevent an abduction.
You should obtain a child travel consent letter granting you permission from the absent parent to leave the country with your child (having it notarized is not required, but highly recommended).
It's important that you give your co-parent notice and preferably get their express permission in writing if you wish to travel outside the state with your child. If the other parent refuses to cooperate, you can ask for the court's permission in advance.