You can claim Head of Household and not claim the child tax credit. Did the child live with him over half the year? Did the father have to sign over the child tax credit because of a divorce decree? I don't know why you even brought up Head of Household when that doesn't matter. All that matters is who claimed the child tax credit. Did he claim it in 2019? Why isn't he in 2020? This is the info we need to be able to give you any useful advice.