Unless a statute, court rule, or court order provides otherwise, yes (you will want to ensure you consult the governing law for your particular jurisdiction). That power to travel out of state with the child may (may) be subject to certain conditions, such as having to give notice to the other parent, but in my experience the noncustodial parent rarely has the power to prevent good-faith travel out of state with the child by the custodial parent.
In the jurisdiction where I practice law (Utah), there is this statute:
Utah Code § 30-3-36. Special circumstances
(1) When parent-time has not taken place for an extended period of time and the child lacks an appropriate bond with the noncustodial parent, both parents shall consider the possible adverse effects upon the child and gradually reintroduce an appropriate parent-time plan for the noncustodial parent.
(2) For emergency purposes, whenever the child travels with either parent, all of the following will be provided to the other parent:
(a) an itinerary of travel dates;
(b) destinations;
(c) places where the child or traveling parent can be reached; and
(d) the name and telephone number of an available third person who would be knowledgeable of the child’s location.
(3) Unchaperoned travel of a child under the age of five years is not recommended.
Utah Family Law, LC | divorceutah.com | 801-466-9277
https://www.quora.com/Can-a-person-who-has-custody-of-a-child-take-that-child-out-of-state