(a) Except as provided by chapter 25 of this title, the right of voting may only be exercised by personal attendance, and no unregistered voter shall be allowed to vote at any primary or election, except by order of the district court. All persons whose names appear on the district register of electors of the polling district shall be permitted to vote, unless it is shown to the satisfaction of the election officers that he no longer resides in the election district; but at a primary a person shall be permitted to vote only on the ballot of the political party in which he is enrolled in the district register.
(b) If a voter has moved his residence from one polling district to another in the same legislative district within 30 days immediately preceding a primary or election, and for any reason his registration has not been transferred to the polling district of his new residence, he shall be permitted to vote only in the polling district in which he is registered and formerly resided. However, at the next election he shall be required to vote at the polling district where he resides.