WASHINGTON  The Supreme Court on Friday agreed to decide whether the First Amendment requires that the names of people who sign ballot-initiative petitions be kept secret.

As in the court’s decision on Wednesday to block the broadcasting of the trial of a challenge to a ban on same-sex marriage in California, the appeal was brought by opponents of such unions who said they feared harassment should their views be made widely known.

The new case arose from an effort to overturn a Washington State domestic partnership law known as the “everything but marriage” act. Opponents of the law gathered more than 130,000 signatures, enough to place a referendum on the November ballot.

Several groups asked the state to turn over the names, under its public records law, and two groups said they intended to post the names on the Internet. Their goal, according to a news release, was to encourage conversations among friends, relatives and neighbors that “can be uncomfortable for both parties.”