(a) Whenever a special tax is levied on real property by any municipality, other than a special tax levied under the provisions of § 7-382, such municipality may by vote of its legislative body provide that any resident of such municipality who is eligible on the assessment date of such special tax for tax relief under § 12-129b with respect to the general property tax to be levied on such real property in the same calendar year, shall be liable only for a prorated amount of such special tax based on the percentage which such resident’s tax liability for said general tax in such municipality bears to the amount such tax liability would be if such resident were not eligible for tax relief under said § 12-129b, provided, if title to the real property is recorded in the name of such resident or his spouse making a claim and qualifying hereunder and any other person or persons, the claimant hereunder shall be liable to pay his fractional share of such special tax levy calculated in accordance with the provisions of this section, and such other person or persons shall pay his or their fractional share of the tax without regard to the provisions of this section. If, at the time the special tax is levied, the mill rate of the ensuing general tax has not been established and the tax levied, the special tax shall be levied in full and the proration herein provided for shall be calculated at the time such general tax is levied. Thereupon any such resident entitled to benefits in accordance with this section shall receive an abatement of the excess special tax levied if such tax has not been paid, or a refund of such excess if such tax has been paid.

(b) § 12-129d shall not be applicable with respect to tax relief provided by any municipality in accordance with the provisions of subsection (a) of this section.