CONCORD, N.H. (AP) — Two advocacy groups sued the state Wednesday over a new law that effectively blocks out-of-state students from voting in New Hampshire unless they establish legal residency in the state.

The state chapters of the League of Women Voters and the American Civil Liberties Union filed a petition in Strafford County Superior Court on behalf of four out-of-state students who attend the University of New Hampshire, Southern New Hampshire University and Keene State College. They argue that the law freezes out eligible voters from participating in the upcoming state and federal elections and asked a judge to block the law’s enforcement.

The law, which was passed over Gov. John Lynch’s veto, requires people registering to vote to sign a statement saying they declare New Hampshire their domicile and are subject to laws that apply to all residents, including laws requiring drivers to register cars and get a New Hampshire driver’s license.

In the past, students could make New Hampshire their domicile for voting purposes while maintaining legal residency in other states. While that is still technically true — the new law doesn’t require them to be ‘‘residents’’ — it makes them subject to all of the approximately 600 laws that go along with residency.

‘‘Students are left with either signing a statement that doesn’t reflect New Hampshire laws or being forced to give up their constitutional right to vote,’’ said Joan Ashwell, election law specialist for the League of Women Voters of New Hampshire.

Claire Ebel, director of the New Hampshire Civil Liberties Union, compared the new law to an unconstitutional poll tax, saying it would discriminate against students who couldn’t afford to register their cars and pay driver’s license fees.

‘‘You cannot single out categories of people and then discriminate among them,’’ she said.

The law’s backers, however, argued that it simply clarified that people should vote where they live.

‘‘A fundamental premise of having elections that reflect the will of the citizens of a community or a state is that those who vote should be those who live in the city or town, and certainly the state, in which they are voting,’’ House Speaker William O'Brien, R-Mont Vernon, said last week when the U.S. Justice Department ruled that the law did not discriminate against racial minorities.

New Hampshire is among a group of states, including Mississippi, Louisiana and Alabama, that are required under the Voting Rights Act of 1964 to submit any election law changes to the Department of Justice to determine whether they would result in racial discrimination. The state came under the act’s purview because of poor voter turnout in 10 towns in the 1968 presidential election and because it still had a literacy test on the books at the time.

A hearing is set for Sept. 19 on the court petition. In the meantime, the groups are deciding whether to also challenge the state’s new voter identification law.

Under that law, voters will be required to show photo identification or sign an affidavit beginning in November’s general election. A wide range of identification, including student IDs, will be accepted this year, but after that only driver’s licenses, state-issued non-driver’s identification cards, passports or military IDs will allowed. Someone without photo identification would sign an affidavit and be photographed by an election official.

Poll workers did a test run during Tuesday’s primary and were supposed to inform voters without identification about the upcoming changes while still allowing them to vote. But Ashwell said her group and others have collected complaints from voters in about two dozen communities, ranging from signs posted at polling places incorrectly stating that IDs were required Tuesday to voters being sent away if they didn’t show identification.