No, unless your child's mother wants to claim your child as a noncustodial parent. Form 8332 is used when the parent that would not otherwise qualify to claim the child does include the child on his/her return. The child can only be claimed by one of you. The person that made more money will have a larger benefit and should claim the child.
These are the rules for claiming a child on your tax return.
If you all three are living together, only you or your child's mother can claim Head of Household. This is an important designation to the IRS. Click on this article to learn more. What is my tax filing status?