Will leaving one nursing home affect Medicaid eligibility for a new nursing home?

My father left a nursing home because he did not like it there but he wants to go to another one. Since he now is living in another state he has to apply for Medicaid benefits again. Will leaving the old nursing home prevent him from getting Medicaid? He left without a signing a dismissal form because they tried to block him and tried to make us pay for a 'gap month'. He is sane, lucid, knows what he wants, and there is no guardianship or power of attorney.