Yes, if there is no custody agreement in place, the father of your child may take them out of state.
Until there is an order of the court in place regarding custody, both parents have equal rights to possession and access of the child. This means that both parents can make decisions regarding the child, including where to go on vacation and whether or not to move out of state with the child. Although these actions may be frustrating, without a court order in place, they do not constitute kidnapping.
If you feel that the other parent of your child is thinking about moving out of the state, the best way to keep them from taking your child with them, is to speak to an attorney about getting a formal custody agreement in place. It is best to get the momentum on your side BEFORE the move, so acting sooner rather than later is key. The courts are much less likely to order that a child be returned to the jurisdiction than they are to order they remain in the jurisdiction.
Once an agreement is in place, the parties’ rights to possession and access to the child will be set by order of the court. Generally, this will include a geographic restriction. For example, a final order in a suit for custody in Harris County, Texas will often include a provision restricting the residence of the child to Harris and contiguous counties. This is quite a large area including Montgomery, Liberty, Chambers, Galveston, Brazoria, Fort Bend, and Waller Counties. A geographic restriction means that if the other parent is the joint managing conservator with the right to designate the residence of the child, they must do so within the geographically designated area. In order to move out of the state, the other parent would first need to file a motion to modify the order asking that the geographic restriction be removed and show that such a move would be in the best interests of the child.
As far as traveling out of the state with the child, often once there is an agreement in place, the only requirement is that the domestic travel take place during their period of possession. Many agreements also require written notice outlining the child’s travel itinerary be provided a certain amount of time prior to the trip. Parties can even go so far as to require that the other parent consent before any domestic travel. For international travel, there may be additional restrictions regarding passports and consent. If there are concerns about the other parent traveling with the child, make sure to discuss them with your attorney so that they can be addressed in the final order.