Persons eligible for relief, who are residents of the state and residents of the county in which they apply for relief, shall be granted relief by the county of their residence, and the state shall pay to the county the state’s share of the cost of the relief.

Persons eligible for relief, who are residents of the state but who are not residents of any county, shall be granted relief by the county in which they apply for relief, and the state shall pay to the county providing the relief the full cost of the relief provided, until such persons have remained in a county for the period necessary to acquire residence in that county.