Conn. Gen. Stat. § 12-81b

Any municipality may, by ordinance, provide that the property tax exemption authorized by any of subdivisions (7) to (16), inclusive, (18), (27) and (29) of section 12-81 shall be effective as of the date of acquisition of the property to which the exemption applies and shall, in such ordinance, provide procedure for reimbursement of the tax-exempt organization for any tax paid by it for a period subsequent to said date and for any tax paid by the prior owner for a period subsequent to said date for which such organization reimbursed such owner on the transfer of title to such property.