Section 19A. The state treasurer shall annually, on or before July first, pay from monies appropriated from the Local Aid Fund for that purpose, to each city or town certified by the board of library commissioners to have met certain minimum standards of free public library service established by said board, an amount to be used for the free public library or libraries of said city or town, to be determined as follows:—

(1) to each town having a population of less than two thousand five hundred, a sum equivalent to the amount appropriated by it for free public library service during the preceding year, but in no event more than one thousand two hundred and fifty dollars;

(2) to each city and to each town having a population of two thousand five hundred or more, a sum not exceeding fifty cents for each resident therein; provided, however, that such city or town appropriates during the preceding year for its free public library service at least one thousand two hundred and fifty dollars;

(3) to each city and town, in addition to the amount specified in paragraph (1) or (2), a sum determined by allocating the remaining available amount among the cities and towns according to the provisions of section eighteen C of chapter fifty-eight.

(4) in addition to the amounts specified in paragraphs (1), (2) and (3), to each city or town whose library is designated a major nonresident lender by said board, an amount for the purpose of offsetting the costs of extending said service to nonresidents. Said amount shall be determined by said board by allocating the sum appropriated for this purpose according to criteria and formulae developed by said board in consultation with the regional public library systems established under section nineteen C.

No city or town shall receive any money under this section in any year when the appropriation of said city or town for free public library services is below an amount equal to the average of its appropriation for free public library service for the three years immediately preceding, increased by two and one-half per cent of said average. Said board may, upon petition of a community, waive aforesaid requirement upon demonstration of fiscal hardship. Said waiver may only be granted by said board in a given fiscal year to not more than ten cities and towns in the commonwealth.

For a joint public library, the board may approve, at the request of the cities or towns served by the joint public library, a single appropriation requirement in determining amounts under this section. The amount shall be calculated by aggregating the appropriations of the cities or towns administering the library. Upon petition by all of the cities or towns served by a joint public library, the board may waive the single appropriation requirement upon a demonstration of fiscal hardship. A joint public library shall be an undertaking of 2 or more cities or towns to provide public library service to their residents through a single administrative entity.