Town and city councils may pass any ordinances, bylaws, and regulations, not inconsistent with law, that they may think proper, in relation to the time of closing shops, saloons, and other places of resort in the evening, within the limits of their respective towns or cities, and may prescribe penalties for their violation, not exceeding twenty dollars ($20.00) for each offense. Notwithstanding the provisions of any general or special law to the contrary, in the event that the 31st day of December in any year falls on a Saturday or Sunday, the time of opening and closing places of resort at which dancing is permitted may be regulated in the following manner:

(1)  If the 31st day of December falls on a Saturday, the time of closing may be determined at not later than three o’clock (3:00) A.M. on Sunday, January 1;

(2)  If the 31st day of December falls on a Sunday, the time of opening may be determined at not earlier than nine o’clock (9:00) P.M. on Sunday and the time of closing may be determined at not later than three o’clock (3:00) A.M. on Monday, January 1;

(3)  If the December 31st falls on any other day of the week, the hour of closing may be determined at not later than three o’clock (3:00) A.M. the following day.