Section 11. In every district established under authority of section ten there shall be a board composed of the mayor or his designee of such city, if any, as may be included in the district and the chairman of the board of selectmen or its designee of each of the towns, if any, included in said district and the town manager or his designee in a municipality with a town council form of government, if any, included in said district. Said board shall appoint, fix the compensation of, and may remove the director of veterans services of said district. Said board may appoint, fix the salary of, and remove, a deputy or assistant to such director, if in the opinion of said board such an officer is necessary.

Said board may determine the expenses of said director and deputy or assistant and of the department under the charge of said director, and may apportion said expenses among the several municipalities comprising such district on the basis of the taxable valuation of said municipalities as last established by the general court as a basis of apportionment for state and county taxes, or on the basis of the population of each municipality in such district based on the most recent federal census, or by any other means determined by a unanimous vote of said board to be fair and equitable to each community. Said board shall promptly thereafter notify the treasurers of said municipalities of such apportionment. Every city or town treasurer so notified shall, annually in December, certify the amount of such apportionment to the board of assessors of his municipality, who shall include such amount in the tax levy of the following year.

Upon order of the district board the city or town treasurer of each of the constituent members of the district shall from time to time pay to the district treasurer a sum or sums not exceeding, in the aggregate, the amount certified by the board as its respective share of the costs and expenses of the district. In case a city or town becomes a member of a district at a time when it is too late to permit an assessment as provided by sections ten to fourteen, inclusive, such city or town may appropriate and pay to the district treasurer an amount representing its proportionate share of the expense of the district for the period ending December thirty-first in the year in which such city or town becomes a member of the district.