stop paying child support due to medicaid

Hi I need to know how i can stop from paying child support back to the state you see I have covered my son since 2004 under my insurance last year my son went to live with his dad well in aug of 2009 he applied for medicaid when he knew my son had full coverage now child support is coming after me to pay it back I need to know if I'm obligated to pay the money back since I've always had full coverage on my son