You do not need any documentation to claim your child on your tax return. You just file normally. Documentation comes later if there is a competing claim. The IRS will tell you what to send (see links below for a preview).
If someone else claimed your child inappropriately, and if they file first, your return will be rejected if e-filed. You would then need to file a return on paper, claiming the child as appropriate. The IRS will process your return and send you your refund, in the normal time. Shortly (up to a year) thereafter, you'll receive a letter from the IRS, stating that your child was claimed on another return. It will tell you that if you made a mistake to file an amended return and if you didn't make a mistake to do nothing. The other party will get the same letter you did. If one of you doesn't file an amended return, unclaiming the child, the next letter, from the IRS, will require you to provide proof. Be sure to reply in a timely manner.
Winner gets the tax benefits; loser gets to pay the IRS back with penalties and interest. The custodial parent (the one the child lives with most of the year) almost always wins. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332) or if it's spelled out in a pre 2009 divorce decree, without conditions. The fact that his right to claim the children is contingent on being current with child support, means the document is not relevant, regardless of the date.
https://www.thebalance.com/claiming-same-dependent-audit-risk-3193030 (
www.eitc.irs.gov/EITCCentral/f886-h-dep.pdf
