A federal judge allowed a challenge Tuesday to New Hampshire’s new voter residency law to continue, though he expressed some doubts about the strength of the case.

The new law, which took effect July 1, ends the state’s distinction between “domicile” and “residency” for voting purposes. That means out-of-state college students who vote in New Hampshire are now subject to residency requirements, such as getting New Hampshire driver’s licenses or registering their cars.

After a two-hour hearing, U.S. District Court Judge Joseph Laplante refused to dismiss a lawsuit filed by the American Civil Liberties Union on behalf of two Dartmouth College students who argue the law burdens their right to vote. The state had argued the students lacked standing to sue, in part because neither of them owns cars.

“I’m not saying this is a particularly strong challenge,” Laplante said. “But the plaintiffs have standing.”

While not delving deeply into the merits of the case, the hearing touched on several of its central arguments. Assistant Attorney General Seth Zoracki argued there is a strong state interest in creating a “community of interest” so that all voters are treated equally. The law doesn’t infringe on anyone’s right to vote, he said, and has no effect on voter eligibility, registration or the casting of ballots.

Laplante pushed back on Zoracki’s argument that any burdens created by the law would be minimal because only about 5,000 people would be affected, saying burden should be measured by the impact on an individual. But he also questioned the ACLU’s argument that the $50 driver’s license fee amounted to a significant burden, and said it’s not unreasonable for someone who drives on the state’s roads to pay toward their upkeep.

Henry Klementowicz, the ACLU’s attorney, said $50 could be a burden to a struggling college student. Beyond that, the law will have a chilling effect, he argued. The judge appeared to give more weight to that point, after repeatedly questioning whether anyone actually would be prosecuted for failing to get a license or registering a car after voting. None of the attorneys could clearly explain how the law would be enforced.

“Here’s the thing: If we can’t think of any ways this law changes election law, and we can’t think of any ways it changes motor vehicle laws, what is this law and what does it do?” the judge asked. “What’s going on here, except maybe some people being discouraged from voting?”

The law was passed when Republicans controlled the Legislature, but Democrats won majorities in both the House and Senate in November and passed two bills this session to essentially negate the changes. Republican Gov. Chris Sununu vetoed one of them Monday. He has yet to act on the other, which creates a carve-out from the motor vehicle requirements for students and other temporary residents,

Sununu also vetoed a bill that would reverse another election law that also is being challenged in court. The law requires additional documentation from voters who register within 30 days of an election. It took effect in 2017 but a judge blocked penalties of a $5,000 fine and a year in jail for fraud while the court challenge is pending.