Ms. Cegavske said the ballot language she used fairly reflected text submitted to her office by those advocating the measure.

“There was no input from the gun industry in the writing of the ballot question,” Gail J. Anderson, the deputy secretary for Southern Nevada, said in a statement.

After a minimum-wage campaign accelerated last year in Ohio, emails show, Jon A. Husted, the secretary of state, communicated with an Ohio Chamber of Commerce affiliate as the business group discussed plans with the restaurant industry to “meet and strategize” about its opposition effort.

A spokesman for Mr. Husted said that “the amendment and referendum processes can be cumbersome” and that “the secretary is often asked to come explain precisely how it works.”

Minimum-wage advocates chastised Washington’s secretary of state, Kim Wyman, who is in the midst of a re-election campaign. She has benefited from a blitz of radio advertisements paid for by the Republican group that sponsored the May meetings with industry representatives. Ms. Wyman declined requests to comment.

At the three-day hunt — where corporate donors and secretaries of state from Kansas, Mississippi, Georgia and Arkansas shared a one-story, wood-frame hunting lodge, with stuffed deer and elk antlers mounted on the walls — there was little discussion of formal election matters.

Instead, it was an opportunity for the corporate executives to cement personal connections. Together, they set loose Labrador retrievers on acres of prime high-grass hunting grounds, flushing pheasants and quail from their hiding spots.