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Form 8332 is for a custodial divorced or separated parent who relinquishes the tax benefit for the dependent to a noncustodial parent. This form wouldn't apply to the situation you described, as noted by @xmasbaby0.

See this IRS webpage for more information on who qualifies for the Child Tax Credit.

To file as head of household, you must furnish over one-half of the cost of maintaining the household for you and a qualifying person. 

Head of Household filing status typically allows parents or adults with qualifying dependents who provide over half the cost of keeping up a home for a qualifying person to claim a higher standard deduction and be taxed at lower tax rates than single taxpayers or those who are married filing separately.

To qualify, you have to meet certain criteria. To file as Head of Household, you have to:

• Pay for more than half of the household expenses
• Be considered unmarried on the last day of the tax year
• Have a qualifying child or dependent

This tax filing status includes single parents and divorced or legally separated parents with custody of the child. Further, you can also be an adult who provides support for a parent or other relative under qualifying circumstances.

The eligibility of a qualifying child or dependent extends beyond just your own son or daughter. To be considered a qualifying child, the child has to meet the criteria in each of the following categories:

• The child is your biological or adopted child, stepchild, foster child, sibling, step-sibling, half-sibling, or a descendant (child, grandchild, great-grandchild, etc.) of one of these relatives
• The child lived within your home for more than six months during the tax year
• The child needs to be younger than you
• As of the end of the tax year, the child is under 19 if he is not a student, or under 24 if he is a full-time college student
• The child did not pay for more than half of their living expenses during the tax year

In some limited cases, you may be eligible to file as Head of Household even if you are unable to claim your child as a dependent. For divorced or separated parents, if the child lived in your home for more than half of the year, you may file as Head of Household, even if the divorce or separation agreement gives the other parent the right to claim the child as a dependent. This situation doesn't apply to you, as noted by @DoninGA.

See this TurboTax tips article for more information. 

@MissMLB