Weber County, a majority-Republican community of 260,000 on the eastern shores of Utah’s Great Salt Lake, held its first by-mail election in 2013. The process gained such widespread confidence that by June of this year, more than 99 percent of ballots cast in the primary were placed in the mail or deposited in a drop box.

But something has changed in Weber County, which now requires three full-time phone operators to field calls from residents “suddenly worried about voting by mail,” said Ricky Hatch, the county clerk and auditor.

“Voters refer to ballots being thrown in a ditch, a river and dumpsters,” said Hatch, a Republican. They mention “dogs receiving ballots” and worry about things such as foreign interference and “rogue postal workers.” Some ask about dead people voting, he said.

Similar questions are flooding county offices nationwide, including many where residents have routinely voted by mail, said Hatch, who also chairs the election committee for the National Association of Counties. In many cases, the worries can be traced to baseless or alarmist statements by President Trump and posts on his Twitter feed. Others have been fed by headlines stripped of context and misleading reporting in the mainstream media, according to election administrators, voting rights advocates and experts in online communication.