SEATTLE  At a time when voters in many states are using petitions to qualify ballot measures on issues from gay rights to property rights, a legal dispute over the identity of 138,000 petition signers here is raising new questions about privacy, free speech and elections in the Internet age.

On Tuesday, voters in Washington State will decide whether to extend to registered domestic partners the same rights married couples have, short of marriage. But the campaign over the referendum, placed on the ballot by opponents of same-sex marriage, has been overshadowed by one issue: whether the individual names of the petitioners should be made public, and ultimately, circulated on the Web.

The United States Supreme Court weighed in last week, deciding to let stand a lower court ruling that ordered Washington’s secretary of state not to disclose the names of the signers. The Supreme Court did not rule on the merits of the issue, and it is unclear whether it will.

The case, legal experts say, could chart new territory well beyond Washington State. The United States Court of Appeals for the Ninth Circuit, which had ordered the release of the signatures, said the case presented “novel questions of whether referendum petition signatures are protected speech under the First Amendment.”