Ohio Rev. Code § 751.11
When an infirmary is erected and established in a city for the accommodation of its poor, the director of public safety shall not require the board of county commissioners to receive and provide for persons having no legal settlement within this state, or whose place of residence is unknown, or charge the board with the expense of providing for such persons in the city infirmary. Such director shall furnish relief and support to such persons in the city infirmary, applying therefor, the same as the board is required to do, and shall have the same power as the board to remove such persons to such other city infirmary or county home where the pauper's legal settlement is.
This section applies only to counties in which there is a county home and a city infirmary.
R.C. §751.11