Only the custodial parent, with whom the child lived with more than half the year, can claim Earned Income Credit, Child and Dependent Care Credit and the Head of Household filing status.
A non-custodial parent can claim his or her child as a dependent if the custodial parent has signed either a Form 8332 or a similar statement.
If the non-custodial parent is able to claim his or her child as a dependent, the non-custodial parent will get the dependent exemption as well as Child Tax Credit.
You don't have to have a dependent claimed on your return in order to file as a Head of Household (HoH). You still may be able to file using the status even if the other parent claims the child as a dependent.
HoH status can be claimed by the parent who has custody of more than half of the year. Typically, eligibility is determined by your custody agreement.
To use the HoH status you must meet a series of requirements, including:
You maintain the household in which the child lives, even if they are not claimed as your dependent
You are unmarried at the tax year's end or married and have been living apart from your spouse for over six months
The house you live in must be your own home and in most cases must be the main home of the dependent, meaning they reside in the dwelling for more than six months out of the year
You have to support more than half of the household, meaning you take care of all expenses and costs
You are a U.S. citizen or resident alien throughout the duration of the tax year.
Additionally, you may also qualify for the Child and Dependent Care Credit, Earned Income Credit for those which lower income amounts, and other tax credits you normally claim.
The other noncustodial parent may claim the dependency exemption for the child, if you, the custodial parent, releases a claim to exemption. Also, the noncustodial parent may claim the child tax credit for the child if the requirements for the child tax credit are met.