Mr. Wallace, in a letter to the state board on Thursday, raised the possibility that “serious irregularities and improprieties may have occurred.” He singled out rural Bladen County, which, he wrote, had the highest percentage of absentee ballot requests of any county in the state, 7.5 percent of all registered voters.

It also seemed unusual, he argued, that Mr. Harris received nearly 96 percent of Bladen County’s absentee-by-mail votes in the Republican primary, in which Mr. Harris narrowly upset Representative Robert Pittenger, a Republican who was first elected in 2012.

Mr. Wallace also wrote that Democratic officials were told that a person being investigated by the state was an employee of a consulting firm that worked for the Harris campaign. A lawyer for Mr. Harris’s campaign did not return calls seeking comment.

Certifying the election without a hearing, Mr. Wallace argued, “would be a grave injustice, and a permanent stain on this board and a stain on North Carolina’s national reputation for free and fair elections.”

Dr. J. Michael Bitzer, a politics and history professor at Catawba College, near Charlotte, said it appeared odd that large numbers of requested absentee ballots in Bladen County and neighboring Robeson County were not returned: about 40 percent in Bladen, and 62 percent in Robeson.

“That says, ‘Well, people were either willing to request it but not carry through, or they requested it and something happened on the return — and we just don’t know which is which,” he said.

Included with the letter were several affidavits from Bladen County residents. One of them, Datesha Montgomery, said that she was visited by a young woman around late September who told Ms. Montgomery that she was collecting ballots. “I filled out two names of the ballot, Hakeem Brown for sheriff and Vice Rozier for board of election,” Ms. Montgomery wrote. “I gave her the ballot and she said she would finish it herself. I signed the ballot and she left. It was not sealed up at the time.”