My fiancé , our daughter and myself live together in a home I own. My fiancé currently claims our daughter. Can I still claim head of household ?

[xmasbaby0]

No.  If all of you live together then only one of you can enter anything about the child on your tax return.   If your GF claimed the child then you do not enter anything about the child on your own return--which means you file as Single---not HOH.

[Opus 17]

The ability to “split” the benefits of a child dependent only applied to children of parents who are divorced or separated and sharing custody. In TurboTax, when it asks if you have a custody agreement with the other parent, you need to answer no in your situation, because this question only refers to a legal agreement between parents who are divorced or separated and living apart.

If one parent answera “yes” that they have a custody agreement, they may have been denied certain tax benefits, but the other parent can’t claim those benefits if the two parents are living together.

In your situation, one parent must claim that as a dependent and answer “no” to the custody question, and the other parent should not list a child on their tax return at all. The parent who paid more than half the expenses of the home could claim the child and file as head of household, or the parent who claimed less than half the household expenses could claim the child and file as single. The parent who does not claim a child will also have to file as single.