(a) All real property in the district shall be taxed to the owners, whether individuals, copartnerships, or corporations, according to the last valuation made by the assessor of taxes of the town of Charlestown, prior to the next assessment, adding, however, any taxable real property which may have been omitted by the assessor of taxes of the town of Charlestown or afterwards acquired, and in all cases where the town assessor may have included property within the district and property without the district in one valuation, the tax assessor of the district shall make an equitable valuation of that portion of the property lying within the district.
(b) In assessing and collecting taxes, the proceedings shall be had by the officers of the district, as near as may be, as are required to be had by the corresponding officers of towns in the state in assessing and collecting town taxes.