Two in every three Utah voters back the campaign to legalize medical marijuana in the state, according to a new Salt Lake Tribune-Hinckley Institute of Politics poll.

Support for the measure remains high, though the survey shows some voters have changed their minds in recent months, when a group that included top Republican politicians sounded off against the measure.

Some 66 percent of voters say they support the initiative, which would legalize marijuana possession and use for approved patients with ailments like cancer and chronic pain. That’s a drop from a Tribune poll in January, when 76 percent said they somewhat or strongly supported the measure.

That dip follows consistent polling showing support over 70 percent. (In January, 76 percent of respondents told The Tribune they supported the measure. In October, 75 percent supported it.)

It also shows the influence the LDS Church has over Mormons in a state where nearly half of all voters are active members of the religion.

Christopher Cherrington | The Salt Lake Tribune

What remains to be seen is whether the predominant faith will come out more strongly against the measure than its indirect statements of concern so far.

“This is not a hill they want to die on,” said Matthew Bowman, an associate professor of history at Henderson State University (Arkansas) who also wrote a book on the Mormon faith.

Bowman recalled the church’s attempts in the 1930s to prevent Utah politicians from ratifying an amendment to repeal alcohol prohibition in the United States. The state cast the deciding vote in favor of allowing alcohol sales after nearly 15 years prohibiting it.

As the marijuana measure continues to poll well, and as church members continue to believe marijuana should be used for medical — rather than recreational — purposes, Bowman said the church may avoid directly calling on its members to oppose the initiative.

“The church is often pretty hands-off when it comes to political issues,” Bowman said. “It very rarely weighs in on stuff like this, [and] when it does it is often rather like this. A general statement of principles.”

The LDS Church leadership has expressed concerns with the medical marijuana initiative, while stopping short of directing members to vote against it.

A legal analysis prepared by church attorneys, Mormon leaders wrote in a statement, “raises grave concerns about this initiative and the serious adverse consequences that could follow if it were adopted.”

Still, the statement encouraged members to read the legal opinion for themselves and “to make their own judgment.”

The Tribune asked poll respondents whether the church’s input changed their minds on the initiative. The results show while the feedback changed the minds of 29 percent of voters who consider themselves “very active” Mormons, it had no effect on 58 percent of “very active” LDS voters.

In fact, 11 percent of respondents said they were more likely to support the initiative because of the statements from The Church of Jesus Christ of Latter-day Saints, including 8 percent of very active Mormons.

Sixteen percent of all respondents said they were less likely to support the initiative because of the church’s position, and 61 percent said the stance had no impact. Eleven percent said they didn’t know what the church’s position meant for them. The poll was conducted by the Hinckley Institute between June 11-18 and has a margin of error of plus or minus 3.8 percentage points.

Political watchers said it appeared the church would largely stay on the sidelines, without explicitly telling members to oppose the measure, as it did with an anti-gay marriage constitutional amendment that California passed in 2008.

“This is one of these issues that I think the church leadership always tends to be relatively cautious about,” said Matthew Burbank, a political scientist at the University of Utah, who assisted on the poll. “It doesn’t go to the heart of their kind of religious concerns in the same way that something like the question of marriage equality did.”

Officials with the LDS Church declined to comment on their statements, the results of the latest poll or whether leadership intended to weigh in and spend money in an attempt to defeat the initiative.

DJ Schanz, campaign director of the Utah Patients Coalition, conceded the church’s influence is “undeniable,” but said the campaign was “encouraged” by the latest poll.