Supreme Court justices seemed split Monday on whether a federal law intended to streamline voter-registration procedures means that states may not attach additional requirements, such as proof of citizenship.

The federal registration form that Congress says states must “accept and use” requires only that the applicant swear under oath that he or she is a citizen.

But Arizona voters in 2004 passed a requirement that applicants provide additional proof beyond that statement. The U.S. Court of Appeals for the 9th Circuit ruled against the state, saying Arizona could not add requirements to the federal form.

The state-by-state battle over who is eligible to vote, what kind of identification or proof may be required, and even the hours of voting prompted a host of legal battles leading up to the 2012 elections. In general, Republicans proposed new restrictions as necessary to combat voter fraud, while Democrats said such moves would harm minorities and the poor, who often do not have easy access to the required credentials.

The oral arguments Monday hardly reflected those incendiary partisan battles — there was an extended discussion about whether “may require only” really means “shall require only.”

The U.S. Supreme Court building in Washington. (J. Scott Applewhite/AP)

Still, a ruling for Arizona could open the door for states to add requirements to the federal registration form, and the issue seemed to split the court along familiar ideological lines.

Arizona Attorney General Thomas C. Horne (R) told the court that the National Voter Registration Act required the development of the federal form that applicants may mail in to register to vote but that the law was not meant to limit what the states could require.

“It is the burden of the states to determine the eligibility of the voters,” Horne said, adding that Congress did not specifically tell states not to demand proof of citizenship.

“Congressional silence should not disable states from taking sensible precautions to exclude noncitizens from voting,” he said.

He immediately ran into trouble from liberal justices Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan.

Ginsburg said Congress was not silent about citizenship. It had decided that a sworn statement subject to perjury charges was sufficient, she said.

“So it’s not as though the federal form didn’t relate to citizenship. It did,” Ginsburg said. “And it said this is the way we deal with citizenship. Then Arizona adds something else.”

Justice Anthony M. Kennedy, who might be in a pivotal position given the divided reactions of his colleagues, asked Horne if Arizona could add other requirements.

When Horne said yes, if they were consistent with the objectives of the act, Kennedy said it then seemed to him that the federal form “is not worth very much.”

On the other hand, Kennedy said the appeals court used a test that “ignores the proposition that the state has a very strong and vital interest in the integrity of its elections, even when those, and perhaps especially when those are elections of federal officials.”

Retired Justice Sandra Day O’Connor, who still hears cases in the lower courts and was part of a panel ruling against Arizona in this one, watched Monday’s proceedings from the front row.

Patricia A. Millett, who is representing groups challenging the law, said Congress’s intent was to reform a system where “40 percent of eligible voters were not registered, because state procedures and burdens were standing as an obstacle.”

“Enclosing your driver’s-license number is that immense barrier, right?” asked Justice Antonin Scalia, referring to one of the ways applicants could satisfy Arizona’s proof-of-citizenship requirement. He said it should be “no problemo” for the state to require what the federal form lacks.

Millett said that only driver’s licenses acquired after 1996 would work. She said the district court found more than 31,000 people were rejected from registration because of Arizona’s law. Of these, she said, 11,000 were eventually registered and Horne had acknowledged there was no reason to believe the 20,000 others were ineligible.

Justice Samuel A. Alito Jr. said it was a “crazy system” for Arizona to be able to require certain information under its own registration procedures but not the federal form.

But Deputy Solicitor General Sri Srinivasan, representing the Obama administration and defending the federal law, said the purpose of the law would be defeated if the form “set a floor, but then each of the 50 states could superimpose whatever additional requirements they wanted.”

The case is Arizona v. Inter Tribal Council of Arizona.