In an episode in Eitzen, Minn., a city of 250 people about 170 miles southeast of Minneapolis along the border with Iowa, a team of workers was “surrounded by three men who refused to accept their identification as public health workers,” Dan Huff, an assistant commissioner at the Minnesota Health Department, said in a statement.

One of the men was armed and the men used “racial epithets” during the confrontation, he said.

“The workers felt that the intention of the men was to intimidate them,” Mr. Huff said.

He said there was a “series of troubling incidents across Minnesota,” including ones in which residents followed and videotaped workers and threatened to call the police on them.