WASHINGTON (CNN) -

Legal challenges to state voter regulations are still drawing political and judicial scrutiny four months after the November election.

This was evident in a divisive oral argument on Monday at the Supreme Court over whether states can enhance a federal voter registration law with their own requirements.

The justices appeared at odds over Arizona's voter-approved Proposition 200 and its insistence on proof of citizenship before registering.

The state calls it a "sensible precaution" to prevent voter fraud. Civil rights groups counter that it adds an unconstitutional and burdensome layer of paperwork for tens of thousands of citizens.

"If I see the purpose of the [federal law] is to simplify registration, how is Arizona's provision consistent with that objective and purpose," said Justice Sonia Sotomayor, given "that many people don't have the documents that Arizona requires?"

But Justice Antonin Scalia spoke for several of his conservative colleagues, asking, "What is -- in the words of the [federal] statute -- 'necessary to enable' for the appropriate state election official to assess the eligibility of the applicant? It's clear that the statute intends the states to be able to do that."

The appeal is a classic federalism issue on the often delicate line between conflict and cooperation between state and federal governments over enforcing voting procedures.

The current fight has produced a range of states, lawmakers, and advocacy groups on both sides of the issue. The Obama administration opposes the law.

Retired justice Sandra Day O'Connor, an Arizona native, was among those attending the hour-long arguments.

Justice Anthony Kennedy last June blocked the Arizona law from being enforced, while the high court decided internally whether to accept pending appeals for review. The ballot measure was passed in 2004 and has been lingering in the federal courts ever since.

The Constitution says the that state legislatures should determine the "times, places, and manners of holding elections for senators and representatives," but Congress has the power to "make or alter such arrangements."

Federal lawmakers did just that in approving the National Voter Registration Act in 1993, which has since been called the "Motor Voter" law.

It was meant to streamline election participation. It requires states to have any application for a driver's license treated also as a voter registration -- the "motor voter." The law also requires states to "accept and use" mail-in and in-person applications.

A federal Election Assistance Commission was created to produce an nationally uniform voter application form, which states must use. Any extra state instructions -- or "add-ons" must be approved by the commission.

The question was whether extra instructions are permitted and just how the federal form must be respected in the first place.

Arizona Attorney General Thomas Horne told the court during Monday's arguments that prohibiting a state from effectively enforcing the citizenship requirement is "so far-reaching that if Congress had intended that, it would have put the prohibition in the statute expressly, which it did not do."

Horne said that inaction by Congress "should not disable states from taking sensible precautions to exclude noncitizens from voting."

That brought quick skepticism from the three female justices, including Sotomayor, who questioned the state's rejection of thousands of mail-in registrations.

"Each state must accept and use the federal form -- period, and not add something to it," Justice Ruth Bader Ginsburg said.

The moderate-conservative Kennedy may prove the deciding vote.