Can my sister move from Colorado to Ohio?

You don't provide enough information to provide a complete answer. Since you don't say what kind of case resulted in what you call "custody", it is not clear what rights the child's father has. Generally, if the father has any rights to be involved in the child's life that will be affected by the relocation, the mother must provide him with notice before leaving Colorado. Then, it will up to the father to decide whether to ask the court for some modification of the parenting time or even to try and prevent the move. Perhaps contacting the guardian ad item will be a quick way to find out whether the last court order created any obligation to notify the father.

This is really a question of Colorado law and the specific details of her custody order. Many orders contain notification requirements before moving, and some even require the permission of the other party or the court. Additionally, some courts have local rules on the subject as well than might not even be readily apparent from state law. Your sister should contact an attorney in the jurisdiction in Colorado where her order was issued and get the answers to these questions before doing anything drastic like moving across the country.