The residential custody order does not give you the right to claim the child as a dependent. IRS rules apply. The number one rule is the child must live with you more than half the year. If the child lived with both the grandparent and the parent for more than half the year, the parent has the higher priority. In that case, the grandparent can only claim the child with the parent's permission AND if the grandparent has a higher income ( AGI) than the parent.
If the child live with you more than half the year and lived with the parent less than half the year, then you can claim him.
