Can a 16-year-old legally move out without parental permission in Arkansas and live with another parent?

Until you turn 18, your custodial parent has the right to determine where you live. If you move in with the non-custodial parent without permission from the custodial parent, then they can call the police and have you picked up and brought back home. The non-custodial parent could be charged with 'interference with custody' and possible other charges as well. The non-custodial parent can petition the court for a change of custody. At your age, you would be allowed to state where you would like to live. The judge will take your wishes--along with many other things--into consideration when making the final decision.