NEW YORK — The Supreme Court’s ruling last month legalizing same-sex marriage nationwide has left Americans sharply divided, according to an Associated Press-GfK poll that suggests support for gay unions may be down slightly from earlier this year.

The poll also found a near-even split over whether local officials with religious objections should be required to issue marriage licenses to same-sex couples, with 47 percent saying that should be the case and 49 percent say they should be exempt.

Overall, if there’s a conflict, a majority of those questioned think religious liberties should win out over gay rights, according to the poll. While 39 percent said it’s more important for the government to protect gay rights, 56 percent said protection of religious liberties should take precedence.

The poll was conducted July 9 to July 13, less than three weeks after the Supreme Court ruled states cannot ban same-sex marriage.

According to the poll, 42 percent support same-sex marriage and 40 percent oppose it. The percentage saying they favor legal same-sex marriage in their state was down slightly from the 48 percent who said so in an April poll. In January, 44 percent were in favor.