You can't. That isn't what Form 8332 is for. Form 8332 is for a non-custodial parent who wants to release his or her claim for a child to the other parent.
If you are a qualifying dependent of another person, meaning that you are related to them and that they provide more than half of your support, then they can claim you as such and they do receive credits for you on their tax return, regardless of what they tell you. They receive $500 "credit for other dependents".
If you are not a qualifying dependent of another person, simply print out your return and file it by mail and the IRS will later mail a letter to you and anyone else who listed you on their tax return requesting proof of the claim that you are a dependent (or not a dependent in your case) and they will sort it out.
The person whose return is not correct will have their return adjusted and will be required to pay back the tax plus penalties and interest.
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