Section 31. The county commissioners shall apportion and assess all county taxes among and upon the several cities and towns according to the most recent equalization and apportionment reported by the commissioner of revenue to the general court pursuant to section ten C of chapter fifty-eight, and shall, by their clerk, certify the assessments to the assessors thereof. The several amounts so apportioned and assessed shall be collected and paid similar to that of the state tax into the respective town treasuries, and the commissioners in their warrants shall require the selectmen or assessors of each town to pay, or to issue their warrants requiring the treasurer thereof to pay, to the county treasurer the amount so assessed. The county commissioners shall prescribe that one half of the total certified assessment of each city and town shall be paid on November first of each year and the remaining one half of such assessment shall be paid on May first of the next year. The selectmen or assessors of each city and town shall return a certificate of the name of the treasurer of such city or town, with the sum which he may be required to collect, to the county treasurer within the time fixed by the warrant of the county commissioners in accordance with the provisions of this section.