WASHINGTON — People in the United States are evenly divided over the Supreme Court case that made same-sex marriage legal nationwide, according to an Associated Press-GfK poll this month.

Many think local officials with religious objections to marrying gay and lesbian couples should be exempt from issuing licenses.

Altogether, 39 percent approved of the court’s decision and 41 percent disapproved. Another 18 percent neither approved nor disapproved.

Poll respondents were divided over allowing same-sex marriage in their own state, with 42 percent in favor and 40 percent opposed.

The poll found no surge in support for same-sex marriage since the court’s ruling June 26. If anything, support was down slightly since April, when 48 percent said they were in favor in another AP-GfK survey.

As marriage rights for gay couples become settled law, divisions exist over how the law should handle those who have religious objections to same-sex marriage.

When the two are in conflict, 56 percent of those questioned said it’s more important for the government to protect religious liberties, while 39 percent said it’s more important to protect the rights of gays.

People were split over whether officials who issue marriage licenses should be allowed to say no to gay and lesbian couples because of religious objections. Just under half said those officials should not have to issue the licenses, about the same proportion saying they should.

Also, 59 percent think wedding-related businesses should be allowed to refuse service to same-sex couples, compared with 52 percent in the earlier poll. By comparison, 46 percent said businesses in general should be allowed to refuse service because of their religious principles, while 51 percent said that should not be allowed.

Self-described members of Protestant denominations were more likely to oppose than favor same-sex marriage, 52 percent to 32 percent.

Catholics were more likely to be in favor than opposed, 48-32. Seven in 10 evangelical Christians opposed allowing same-sex couples to marry legally. On the other hand, 56 percent of those who do not belong to any religious denomination said they were in favor.

Also, 60 percent of Protestants, 48 percent of Catholics and 76 percent of evangelicals said local officials should not have to issue marriage licenses to same-sex couples. Just 37 percent of those with no religious affiliation agreed.

The survey found a gulf between Democrats and Republicans.

Most Democrats said it was more important for the government to protect gay rights, 64 percent to 32 percent. Most Republicans said it was more important to protect religious liberties than gay rights, 82-17..