Ohio Rev. Code § 2117.41
A claimant whose cause of action accrues as provided in section 2117.37 of the Revised Code may bring suit to recover on the claim against the heirs, next of kin, surviving spouse as next of kin, devisees, and legatees under the decedent's will, each of whom shall be liable to the claimant in an amount not exceeding the value of the real and personal property that the person received under the will or on distribution of the estate. If, by the will of the deceased, any part of the estate or any one or more of the devisees and legatees is made exclusively liable for the debt, in exoneration of the residue of the estate or of the other devisees or legatees, the terms of the will shall be complied with in that respect and the persons and estate so exempt by the will shall be liable for only so much of the debt that cannot be recovered from those first chargeable with the debt.
No suit shall be maintained under this section unless commenced within six months next after the time when the cause of action first accrues, except in case the suit is for the balance due after a payment by the executor or administrator, in which case suit shall be brought within two months after the final payment by the executor or administrator. If the person entitled to bring the suit is under legal disability, the person may bring the action within one year after the person's disability is removed.
If any of those heirs, next of kin, surviving spouse as next of kin, devisees, or legatees dies without having paid the person's just proportion of the debt, the executors or administrators of that deceased person's estate shall be liable for that proportion to the extent the deceased person would have been if living.
R.C. § 2117.41