Unless you have a state recognized legal separation agreement (in which case you could file as Single), you would file as Married Filing Separately. The following states don't recognize legal separation as a status: South Carolina, Georgia, Delaware,Florida, New Jersey, Maryland, Texas, Pennsylvania and Mississippi.
If her father is claiming her as an exemption, and you share custody with him,you may be able to file as Head of Household if she lived with you for more than half the year, but two people can't file as head of household using the same qualifying child.
See this link for more information: https://turbotax.intuit.com/tax-tools/tax-tips/General-Tax-Tips/Guide-to-Filing-Taxes-as-Head-of-Hou...
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