Dependent on SSI

What is the name of your state? NY
My infant grandson ( born prematurely ) is receiving SSI, my daughter doesn't work and is not married. However, the baby's father lives with them and did work last year. The question is: Can he claim the baby and/or Head of Household on his return ?

Probably & yes. He may not be able to claim the boy as a dependent if he did not provide 51% of the boy's support. He can claim your daughter if she lived with him the entire year. He can claim the boy for EIC purposes.