Ohio Rev. Code Ann. § 727.29

When a special assessment is made on real estate subject to a life estate, the assessment shall be payable by the tenant for life, but upon application by the life tenant to a court of competent jurisdiction, by action against the owner of the estate in fee, such court may apportion the cost of the assessment between the life tenant and the owner in fee in proportion to the relative value of the improvement to their estates, respectively, to be ascertained and determined by the court on principles of equity.