Form 8332 is not verbal---it is a signed document.
Are you the custodial parent? Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody? Did one of you sign a Form 8332?
If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit + education credits if the child is a full-time college student. The non-custodial parent gets the child tax credit for children under the age of 17.
As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.
No. You don't need a 8332 form. It is if you are NOT claiming the child and you give it to the other parent to the other parent can claim and file there form with their tax return.