I have on idea about my new state but in OR there was no public PK except Head Start, in which you had to be below the poverty line or bilingual, or Early Intervention. Both are free and Early Intervention is free no matter how much you make. My children went to Early Intervention because of severe speech issues, you would also qualify for other developmental delays, handicaps, autism, etc.
PKs are pretty expensive unless you participate in one that is a co-op