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Let me provide you with the screenshots with the interviews questions my partner is answering.

According to the replies in the thread my partner and I don't need a Form 8332, but how should my partner answer the question below? 

If I click on the question, do I need a legal agreement if both parents live together but aren't married underlined in blue? 

Which parent can claim the dependent on their tax return if we live together but aren't married?
If you're living with the other parent and aren't married and don't have an agreement, the parent who has the highest adjusted income for the year has the right to claim the child on their tax return. However, you're allowed to have an agreement between the two of you about who will actually claim the child. In the case of an agreement, you won't have to fill out Form 8332. Keep in mind, the parent that claims the child as a dependent is the only one allowed to claim all the child-related credits such as the Earned Income Credit and Child and Dependent Care Credit. The other parent should not list the child on their tax return.

If I answer yes, my partner can use Lauren as a dependent. 

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If I answer no to question above under right to claim Lauren as a dependent. It states it turns out Lauren doesn't qualify as your dependent.  Also the federal refund drastically decreases. 

We are not claiming the same daughter on our returns. My partner is filing single. 

How should I answer question regarding do I have custody agreement and Has Lauren's other parent waived the their legal right to you so you can claim her as a dependent on your return this year?