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You have not indicated which parent the child(ren) physically lives with, which can make a big difference.

Be aware that legal custody that a court might grant and *tax custody* are not the same.  It is tax custody  that dictates which parent must sign the 8332 form.   Tax custody is strictly determined by which parent the child physically lived with more than 183 nights in the tax year.  *That* parent is the custodial parent for tax purposes and the non-custodial parent for tax purposes is the other parent.   It is the custodial parent under the tax rules that issues the 8332 to the other parent, or in place of the 8332, the other parent that did not live with the child can use the pre-2009 divorce decree in place of the 8332 if the decree meets the IRS requirements.

The 183 night test applies to each child for each tax year and can change year to year depending which parent the child lived with.   Read the 8332 instructions that define the release.  If *you* were not the parent where the child physically lived then *you* would not provide a 8332 to the other parent since you were not the custodial parent and you did had nothing to release.   It depends on which parent the child(ren) lives with which you have not said.

8332 form and instructions:
<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/f8332.pdf">https://www.irs.gov/pub/irs-pdf/f8332.pdf</a>

Also many (or most) pre 2009 divorce decrees decrees do not meet the IRS requirements to be used in place of a 8322.

See IRS Pub 17
<a rel="nofollow" target="_blank" href="https://www.irs.gov/publications/p17/ch03.html#en_US_2016_publink1000170897">https://www.irs.gov/pub...>

The decree or agreement must state all three of the following.

   1. The noncustodial parent can claim the child as a dependent without regard to any condition, such as payment of support.
   2. The custodial parent will not claim the child as a dependent for the year.
   3.The years for which the noncustodial parent, rather than the custodial parent, can claim the child as a dependent.

  The noncustodial parent must attach all of the following pages of the decree or agreement to his or her tax return.

    * The cover page (write the other parent's social security number on this page).
    * The pages that include all of the information identified in items (1) through (3) above.
    * The signature page with the other parent's signature and the date of the agreement.

I would suggest that you review the special rules for divorced or separated prents that live apart in Pub 17 that I referenced and the detailed 8332 instructions that also deal with it to see if the rules have been correctly applied in your case.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**