Within the Hamilton County Plan Commission jurisdictional area farm structures do require a permit. The following is taken directly from the Ordinance:
Accessory farm structures constructed in the normal course of agricultural business for the support of individual farms are not subject to requirements for detailed construction plans; however, a special agricultural accessory building permit is required with two inspection fees. If any structure requires plumbing, heating, sewage, electrical installation, or office space such structure will be subject to the accessory permit fees contained in the ordinance.
For additional information, please view the Agricultural Related Permit (PDF).