A central question in the case was whether a failure to vote could be the reason to send out the notice.

Ohio is more aggressive than any other state in purging its voter rolls. After skipping a single federal election cycle, voters are sent a notice. If they fail to respond and do not vote in the next four years, their names are purged from the rolls.

A few other states use similar approaches, but not one of them moves as fast. “Ohio is the only state that commences such a process based on the failure to vote in a single federal election cycle,” said a brief from the League of Women Voters and the Brennan Center for Justice. “Literally every other state uses a different, and more voter-protective, practice.”

At Wednesday’s argument, Eric E. Murphy, Ohio’s state solicitor, said about eight states send out notices based on the failure to vote.

Justice Ruth Bader Ginsburg said there was good reason to think that “Congress didn’t want failure to vote to be a trigger for this procedure.”

But Justice Samuel A. Alito Jr. said the laws appeared to permit Ohio to use its notification process.

“Why isn’t the best interpretation of this that one cannot be removed from the list solely because of failure to vote?” he asked. The failure to respond to the notice, he suggested, was an additional reason.