(a) If any applicant for admission as an elector in any town has previously been admitted as an elector in any other town in this state, or in any other state, the District of Columbia, the Commonwealth of Puerto Rico, American Samoa, the Virgin Islands, Guam or the Trust Territory of the Pacific Islands, he shall, under penalties of perjury, so declare, and shall also declare by what name and in what town and state, district or territory he was last admitted as an elector and the street address from which he last voted therein. The admitting official shall within forty-eight hours thereafter transmit a notice of cancellation of such registration, upon a form prescribed by the Secretary of the State to the registrars of such other town or, in the case of a town in another state, district or territory, to the appropriate registration official or officials in such other town. Upon receipt of such notice of cancellation of registration, the registrars of the town from which such elector has removed shall forthwith erase the name of such elector from the registry list of the town, if the same has not been erased therefrom.

(b) When the Secretary of the State receives information from a registration official of another state, the District of Columbia, the Commonwealth of Puerto Rico, American Samoa, the Virgin Islands, Guam or the Trust Territory of the Pacific Islands that an elector of this state has registered in such other state, district or territory, the Secretary of the State may transmit a notification of such registration to the registrars of the town where such individual may be an elector in this state. If the registrars determine that the individual identified in the notice is an elector in this state, the registrars shall remove the name of such elector from the registry list.