One website says this (specifically in regard to Arizona) however, as mentioned below, there very well may be no specific law in Arkansas that you can site and it maybe up to the courts interpretation. Good luck!
Question: Are parents allowed to lock children in their bedrooms? If so, what is the max amount of time allowed?
Answer: Parents have the right and the duty of care, custody and control of their children. They may do whatever is reasonable to exercise their right and duty. The question is whether their action is reasonable and it depends upon the facts of each specific circumstance.
Parents certainly cannot lock a child in a bedroom and then go out to a party. That would place the child in an unsafe situation and would constitute child neglect.
It would probably be unreasonable to lock a child in a room without bathroom breaks for too long a time, or where there is no fresh air, or where there are dangerous fumes or other threats to the health and safety of the child. They would also have to be certain that the temperature in the room was reasonable, and perhaps that water was available. It would probably be unreasonable to lock a child in a room without light, at least in the daytime.
One would also have to consider how often this occurred, and for what reasons the child was locked in their room. If this is the only way that a parent can get this particular child to sit down and do homework, and it only occurs every school day for one hour, it might very well be acceptable. There is no specific law in Arizona regarding acceptable conditions. The matter would be up to a court to decide whether the parent's actions were reasonable.