No. You cannot move out-of-state with the children unless you either have permission from the other parent to do so or get a Court Order granting you permission to move. Many parents don't know this. After all, it's not like the custody police will stop you at the state line and ask for your permission slip. Parents who disobey the law, however, do so at the risk of having to return to Minnesota.
The Minnesota Supreme Court ruled on this issue in 1983. It held that there was a presumption in favor of allowing the custodial parent (i.e., the parent with whom the children reside) to move out-of-state, provided that the purpose of the move was not to interfere with the noncustodial parent's parenting time. The Court explained that it did not want to meddle in the parenting decisions of the custodial parent. To prevent a move, the noncustodial parent was required to show that the move was not in the best interests of the children. This rule was referred to as the Auge presumption, after the case in which it was announced.
In 2006, the law changed dramatically on this issue. The legislature changed who bore the burden of proof. Now, the relocating / custodial parent bears the burden of proof. He/she must convince the Court that the proposed move is in the best interests of the children. By law, the Court must consider eight (8) factors in determining whether the proposed moved is in the child's best interests. These cases present the court with difficult decisions. It must balance the benefit that would presumably come to the relocating parent and the child from the proposed move with the damage that would also be caused to the relationship between the child and the noncustodial parent. There are no easy answers.