A same-sex spouse cannot file using the head of household filing status if they are considered married at the end of the tax year. For federal tax purposes, the terms "spouse," "husband and wife," "husband," and "wife" include individuals married to a person of the same sex if they are lawfully married under state law. Therefore, same-sex spouses are treated the same as opposite-sex spouses for tax purposes.
However, a married taxpayer, including a same-sex spouse, may be considered unmarried and thus eligible to file as head of household if they meet specific criteria. According to the IRS FAQ, a married taxpayer may use the head-of-household filing status if they live apart from their spouse for the last six months of the taxable year and provide more than half the cost of maintaining a household that is the principal place of abode of the taxpayer’s dependent child for more than half of the year.
To summarize, a same-sex spouse can file using the head of household filing status only if they are considered unmarried under the tax rules, which generally requires living apart from their spouse for the last six months of the year and meeting other specific requirements related to maintaining a household for a dependent child.
Sources:
§ 2. Definitions and special rules
Publication 504 (2023)
Rev. Rul. 2013-17
Publication 501 (2023)