My Son and his mother live in my home and I pay for the house,electricity,food, phone, etc I plan to claim Head of House Can he still be a dependent on my taxes and hers

[JhJhhJ]

I want his mom to be able to use him as a dependent. I just want to be able to Claim Head of Household I don't really want the Child tax credit.

[DoninGA]

You cannot have Head of Household filing status if you are not going to claim a qualifying person as a dependent on your tax return.

[xmasbaby0]

You are confusing the rules that can be used for divorced or never married parents who live apart and share custody.  If all of you are living together as a family, then those rules and the "signed agreement" do not apply to your situation.   Only ONE of you can enter the child on your tax return and get the child-related credits.  

One of you files as Single ----with no mention at all of the child on your tax return. The other parent claims the child and the child-related credits including earned income credit, childcare credit, child tax credit----and possibly Head of Household if they paid for over half the support of the household.

If you are not sure which of you that should be--use the IRS tiebreaker rule.

TIE BREAKER RULES

https://itap1.for.irs.gov/owda/0/resource/Commentary_Files_Redirect_ITA/en-US/help/tbrk09.html

If you each try entering the child on your returns, one of your e-files will be rejected.