"she lives with me 6 months of of the year" doesn't establish which one of you is the custodial parent.
For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you
MORE than 50% of the time. One of you has to be the custodial parent and the
other the non-custodial parent. And, yes, the IRS expects you to count the number of nights the child sleeps at each parent's house.
In the rare case (could probably only happen in
a leap year like 2016), where the time that each parent has the child is
exactly equal, then the parent with the higher income (AGI) is the custodial parent, for
the purpose of determining who has first priority on claiming the child as a dependent.
The
custodial parent has first priority on claiming the children on her taxes;
regardless of the amount of support provided by the non-custodial parent. 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.
So, if you are the custodial parent, you do not need to give the father a 8332 and you don't need to get one from him. If he is the custodial parent, you need to get the form from him. The verbl agreement is not enough. https://www.irs.gov/pub/irs-pdf/f8332.pdf
There is a way to split the tax benefits. For future negotiations with the
other parent (and maybe even for this year) the following info may be of use:
There is a
special rule in the case of divorced & separated (including never married) parents.
When the non-custodial parent is claiming the child as a
dependent/exemption/child tax credit; the custodial parent is still allowed to
claim the same child for Earned Income Credit, Head of Household filing status,
and day care credit. This "splitting of the child" is not available
to parents who lived together at any time during the last 6 months of the year;
then only one of you can claim the child for any tax reasons. The tax benefits
may not be split in any other manner.
Note in particular
that the non-custodial parent can never claim the Earned Income Credit, Head of
Household filing status or the day care credit, based on that child,
even when the custodial parent has released the exemption to him.
So,
it's good idea to let the other parent know that you will be claiming those
items, as many first time divorced parents are not aware of this rule and may
try to claim those items, which will cause the IRS to send out letters.
Ref: http://www.irs.gov/publications/p17/ch03.html#en_US_2014_publink1000170897
