Do you all live together as a family? Then NO you cannot split the child-related credits between two tax returns. The form your BF might have seen and been confused by (form 8332) is for divorced or never-married parents who do not live together and share custody of a child.
If you are all living together then only one of you can claim the child. The other one files Single and does not enter anything about the child on a tax return. You can try figuring it out both ways and see how it comes out best----the parent who paid over half the costs of the household could file as Head of Household and claim the child to get the earned income credit, child tax credit and childcare credit. And then you could work out a friendly way to share.
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