Can a non custodial parent claim our son on his taxes

by Crystal
(Akron, Ohio)

I have my son 100% with the other "parent" never even seeing him. He is currently in arrears in child support and wants to claim him on his taxes. Can he claim him and would he need permission from me to do it first? And I do not want him to have her SSN for fear he will do crazy things with it. Do I need to contact someone to stop it or is it possible the state has already handed it over?