The governing body of any county, city or town may provide by ordinance that all taxable real estate or personal property and machinery and tools therein be assessed as of July 1 of each year, any other provision of law, general and special, including the provisions of the charter of any city or town, to the contrary notwithstanding. In any such locality, public service corporation property shall continue to be assessed at its value as of January 1, prior to such assessment date. Any ordinance adopting a July 1 tax day for personal property as authorized hereunder shall require that a prorated refund or credit of personal property tax be given for that portion of the tax year during which the property was legally assessed by another jurisdiction in the Commonwealth and the tax paid. Any locality providing for the taxation of certain property on a proportional monthly or quarterly basis as authorized by general law or special act shall provide for a refund or credit of personal property tax for any tax year or portion thereof during which the property was legally assessed by another jurisdiction in the Commonwealth and the tax paid.