Unless the other parent agrees, you may not move the residence of your child to another state without court approval.
Until very recently, Minnesota law presumed that moving to another state with the custodial parent was in the best interests of the child and it was pretty easy to get court permission. Now, however, the burden of proof is on the custodial parent asking for permission to move the child to another state. The parent asking for permission must now prove that it is in the child's best interests (not the parent's best interests) to be separated from the non-custodial parent. It is not an easy hill to climb and the courts are following the rule very closely. You need some pretty extraordinary circumstances to convince a judge that moving your child away from the other parent is in the child's best interests.
Unless there is a negotiated agreement that you will continue to reside in a specific area of Minnesota, you can move anywhere in the State with your child without having to get the consent of the other parent or the permission of the court. Caution should be exercised in making such a move, however, from a purely "best parenting efforts" standard. Your child needs both of his or her parents to be as active in his or her life as possible. Creating physical distance by moving to another part of the State may be harmful to the relationship your child has with the other parent.