Yes. Form 8332 is the correct form.
The custodial parent signs a Form 8332, Release of Claim to Exemption for Child of Divorced or Separated Parents, or a substantially similar statement, and provides it to the NONCUSTODIAL parent who attaches it to his or her return.
If the CUSTODIAL parent releases the exemption, the CUSTODIAL parent may not claim the Child Tax Credit.
If you need additional blank Forms 8332, you can download them from www.irs.gov/pub/irs-pdf/f8332.pdf
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After a divorce decree is issued, one parent is awarded custody of the child, or perhaps there is dual custody.
The parent given custody of the child is called the custodial parent. The other parent is called the non-custodial parent.
This does not mean that the child is only living with the custodial parent; more likely, the child resides often with each parent throughout the year.
You, as the court designated parent with custody,would be the one to prepare the Form 8332 which allows the other parent to claim the child as an exemption.
The IRS does not want to see both parents claiming an exemption for the same child; therefore, they look to the Form 8332 as the custodial parent's permission for the child to be claimed by the other parent.
I hope this clarifies things. You have been correctly addressing this issue from the beginning with the preparation of the Form 8332. The other parent will attach that Form 8332 to his tax return to show that he has permission to claim the exemption for the child.