(A) A regional transit authority created under sections 306.30 to 306.53 of the Revised Code, shall be exempt from and shall not be required to pay any taxes on property, both real and personal, belonging to any such authority, which is used exclusively for any public purpose. However, except as provided in division (B) of this section, such exemption shall not apply to any property belonging to any authority while a private enterprise is a lessee of such property under written lease providing for tenancy for longer than one year.
(B) The property tax exemption under this section applies to a transit facility that is the subject of an agreement under division (AA) of section 306.35 of the Revised Code, so long as the transit facility is used by the regional transit authority exclusively for a public purpose.