WASHINGTON—The Supreme Court appeared divided Wednesday over an Ohio program that deletes citizens from the voter rolls if they don’t cast ballots over a two-year period and then fail to respond to a mailed notice from the secretary of state.

Federal law prohibits states from disqualifying voters because they sit out elections. But it also encourages states to clean up the voting rolls by removing individuals who have moved, died or otherwise lost eligibility to vote at their registered addresses.

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