Dependent and Medicaid

Can an adult parent who has no earnings (unemployeed) qualify for Medicaid and be my dependent on my tax return without repercussions to me?

 

I.e., can I be forced to pay for their healthcare if they are my dependent?

 

If I do not claim them as my dependent, can they then receive Medicaid if I provide their shelter (they live in my house)?

 

This is in NEW HAMPSHIRE.

 

Thanks