"Releasing an Exemption" is referring to a Custodial Parent relinquishing his or her right to claim the Exemption for their Child to the Non-Custodial Parent. A child's Custodial Parent is the Parent who has custody of the child the greater portion of the year.
"Releasing an Exemption" is accomplished by having the Custodial parent fill out and sign Form 8332, Release/Revocation of Release of Claim to Exemption for Child. The Non-Custodial Parent would then attach this Form 8332 to their Tax Return.
For example, let's say your son lived with you the whole year but you are allowing his father to claim his Exemption for the year. You would fill out and sign Form 8332 and give it to your son's father in order to allow him to claim the Exemption for your son, even though he primarily lived with you.
Check out the TurboTax FAQ below for more details:
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