WASHINGTON — Supreme Court justices disagreed Monday over whether states can require would-be voters to prove they are U.S. citizens before using a federal registration system designed to make signing up easier.

Arizona and other states told the justices the precaution is needed to keep illegal immigrants and other noncitizens from voting. But some justices asked whether states have the right to force people to document their citizenship when Congress ordered the states to accept and use federal “motor voter” registration cards that only ask registrants to swear on paper that they are U.S. citizens.

“I have a real big disconnect with how you can be saying you’re accepting and using, when you’re not registering people when they use it the way the federal law permits them to,” Justice Sonia Sotomayor said to Arizona Attorney General Thomas C. Horne.

Said Horne: “It is the burden of the states to determine the eligibility of the voters.”

This is the second voting eligibility issue the high court is tackling this session. Last month, several justices voiced deep skepticism about whether a section of the Voting Rights Act of 1965, a law that has helped millions of minorities exercise their right to vote, especially in areas of the Deep South, was still needed.

The court will make decisions in both later this year.

In Monday’s case, the court is deciding the legality of Arizona’s requirement that prospective voters document their U.S. citizenship in order to use a registration form produced under the federal “motor voter” registration law. The 9th U.S. Circuit Court of Appeals said that that 1993 National Voter Registration Act, which doesn’t require such documentation, trumps Arizona’s Proposition 200 passed in 2004.

Arizona appealed that decision to the Supreme Court.

The case focuses on Arizona, which has tangled frequently with the federal government over immigration issues involving the Mexican border. But it has broader implications because four other states — Alabama, Georgia, Kansas and Tennessee — have similar requirements, and 12 other states are contemplating such legislation.

The federal “motor voter” law, enacted in 1993 to expand voter registration, requires states to offer voter registration when a resident applies for a driver’s license or certain benefits. Another provision of that law — the one at issue before the court — requires states to allow would-be voters to fill out mail-in registration cards and swear they are citizens under penalty of perjury, but it doesn’t require them to show proof. Under Proposition 200, Arizona officials require an Arizona driver’s license issued after 1996, a U.S. birth certificate, a passport or other similar document, or the state will reject the federal registration application form.

Justice Antonin Scalia seemed to think that a sworn statement wasn’t enough to allow people to register to vote.  “If you’re willing to violate the voting laws, I suppose you’re willing to violate the perjury laws,” he said.

But lawyer Patricia Millett, representing those challenging the law, answered that courts accept sworn statements as proof in criminal cases, some of which end in executions. Congress decided that a sworn statement with the risk of perjury was sufficient to register to vote in the federal system, she said. “This is not just a ticket into the state’s own registration process so they can go, ‘Thank you very much, (throw) it in the garbage can, now do what we would like you to do.’ It is a registration form,” Millett said.

The Arizona requirement applies only to people who seek to register using the federal mail-in form. The state has its own form and an online system to register to vote when renewing a driver’s license. The appeals court ruling did not affect proof of citizenship requirements using the state forms.

Justice Samuel Alito asked if Arizona kept two different voter rolls, one for people who used the state system and one for those who use the federal. The answer was no.

That means that some people face one set of requirements to vote, and others a different set, he said. “This seems to me like a crazy system,” Alito said.

Opponents of Arizona’s law see it as an attack on vulnerable voter groups such as minorities, immigrants and the elderly. They say they’ve counted more than 31,000 potentially legal voters in Arizona who easily could have registered before Proposition 200 but were blocked initially by the law in the 20 months after it passed in 2004. They say about 20 percent of those thwarted were Latino.

But Arizona officials say they should be able to pass laws to stop illegal immigrants and other noncitizens from getting on their voting rolls. The Arizona voting law was part of a package that also denied some government benefits to illegal immigrants and required Arizonans to show identification before voting.

Checks since last fall by The Associated Press showed that in Colorado, election officials found 441 noncitizens on the voter rolls out of nearly 3.5 million voters. Florida officials found 207, or 0.001 percent of the state’s 11.4 million registered voters. In North Carolina, 79 people admitted to election officials that they weren’t citizens and were removed from the rolls, along with 331 others who didn’t respond to repeated inquires.

Horne compared the Arizona system to an airline sending out e-tickets instead of paper tickets but asking for identification before allowing passengers to board the airplane. “That would not contradict the statement that they are accepting and using e-tickets,” he said.

But Justice Elena Kagan didn’t accept that analogy, saying Arizona went further. “Wouldn’t it contradict it if instead of saying ‘Well, we’d like you to offer identification,’ saying, ‘Well, we’d like you also to have a paper ticket’?” she said.

Arizona asked the federal government to add the state’s citizenship eligibility requirements to the federal form but was turned away. Scalia said the state should have sued to overturn that decision. “Why didn’t you do that?” said Scalia, who indicated that he would look favorably on such a challenge.

The decision not to challenge was his predecessor’s, Horne said.

The case is 12-71, Arizona v. Inter Tribal Council of Arizona, Inc.