How to get a document stating I do not have to pay child support?

You and the mother can sign an agreement that says that she waives child support and that you don't have to pay. However, such an agreement is not enforceable, meaning that you can sign anything you want to sign but it is not binding on a court. It is the child's right to be supported by both of his parents, and mother cannot simply release that right. There are certain circumstances where a court might uphold some agreement regarding paying child support that is less than would otherwise be due, but that does not sound like the situation you are describing.