I have a daughter. My partner and I are not married, so she is going to do hers with our daughter. When they ask me if I have dependents, should I put no?

[MindyB]

Yes, that is correct.  You should answer "no." ‌A dependent may not be claimed by 2 different individuals filing separate tax returns.

Here's some more information on dependents you may find helpful: Rules for Claiming Dependents on Taxes

[Hal_Al]

If you and the other parent live together, either one of you (but not both) may claim the child. You may decide between you which one will claim the child. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice. It may be worthwhile to prepare trial returns, both ways,  to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.

A common error is when unmarried parents live together,  If you and the other parent live together, only one of you can claim the child for any tax benefit. The TurboTax interview is confusing (it's designed for divorced parents, who are allowed to split the child). The second parent should not enter the child, at all.

In order to claim Head of Household  (HoH)  filing status, you must be claiming a dependent and you must be the partner that paid more than half of the household expenses.