The wife can use MFJ if the husband is willing to also sign the tax return and she is willing to accept any tax and reporting liability for the husband.
The wife MAY qualify to use Head of Household filing status if she did not live with her husband at any time during the last 6 months of the tax year AND she paid more than 50% of the cost to support the household in which she and her dependent child lived for more than 6 months of the tax year. The child need not be a dependent on her own return if she is allowing the father to claim the child by use of Form 8332.
The wife may also elect to use MFS filing status. She will lose the ability to claim her dependent care credit, earned income credit, but will still retain child tax credit.
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