Ohio Rev. Code § 2945.52: Counsel appointed shall represent the defendant.

Counsel assigned by the court to represent the defendant may attend upon and represent the defendant at the taking of a deposition under section 2945.50 of the Revised Code, and said counsel shall be paid a reasonable fee for his services in taking such deposition, in addition to the compensation allowed for defending such defendant, to be fixed by the court. He shall also be allowed his actual expenses incurred in going to and from the place of taking the deposition.