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@kyliedrake28 --

If the child lived with you more than half the year, then by IRS rules you are the custodial parent and you have the right to claim him/her. 

If you wish to allow the non-custodial parent to claim the child, then you must furnish them with a signed IRS Form 8332, which they must submit with their own tax return.  Here's a link to that form:

https://www.irs.gov/pub/irs-pdf/f8332.pdf