Anyone registering to vote attests that he or she is a citizen, but Ohio Secretary of State Jon Husted said mass registration drives often aren’t able to give due attention to that part, and so illegal immigrants will still get through.

Kansas Secretary of State Kris W. Kobach said even some motor vehicle bureau workers automatically ask customers if they want to register to vote, which some noncitizens in the past have cited as their reason for breaking the law to register.

“It’s a guarantee it will happen,” Mr. Kobach said.