Conn. Gen. Stat. § 12-170i

(b) Any person eligible for tax relief pursuant to this section shall: (1) If the tax has been paid for any year for which the tax was imposed after the death of the preceding taxpayer, be reimbursed by any municipality collecting any such tax in an amount equal to the difference between the amount of tax which would have been paid by such person if such person had been the owner of such property as of the date of the determination of eligibility for tax relief pursuant to this chapter and the amount actually paid; or (2) if such tax has not been paid for any such year, pay a tax equal to the amount which would have been imposed if such person had been the owner of such property as of the date of the determination of eligibility for tax relief pursuant to this chapter.

(c) The determination of eligibility of any person for tax reimbursements or credits pursuant to this section shall be made in accordance with the procedures set forth in this chapter, except any person may apply for such relief at any time within one year of the final settlement of the estate of the deceased taxpayer or one year of July 1, 1985, whichever is later.

(d) The state shall reimburse each municipality by the last day of each calendar year in which tax reimbursements were paid or tax credits were granted pursuant to this section to the extent of the total revenue loss represented by such reimbursements or credits.