Twigg acknowledged being at a meeting about a year ago but declined to discuss specifics. Twigg said all the people who were involved should explain together what happened rather than leaving it up to him.
"There's probably going to be a couple different stories told here. If I answer these questions, it's going to look political," Twigg told Mario.
"There is an issue out there festering. If and when I get into a situation where I have to answer specific questions, I will answer them," Twigg said on the radio.
After the show, Twigg said the meeting was about how the city treasurer's job would be filled. Several people at the meeting wanted to be treasurer, and Twigg said he was asked whether he would be willing to give the post to someone else after a year.
Twigg, who is treasurer, said he disagreed with the idea.
The issue came up again at the June 12 council meeting.
"I told the mayor I'm not making any deals," said Twigg.
Mayor Earnest L. Sparks said he recalls a conversation about the treasurer's job about a year ago, but that there was no organized meeting. Sparks said the discussion was held "on the street."
Council Member Richard Yauger said he recalls a meeting a year ago with council member Max Parkinson, Merle Butts, Sparks and Twigg in an office in town.
Yauger would not say where the office was located. Yauger said he believes there were two other people there. He said there was not a quorum of the council present.
"I wouldn't have attended it if it would have been. I'm very sensitive to that," said Yauger, who said he can't remember what was discussed at the meeting.
West Virginia's open meetings law requires each public body to notify the public of the time and place of regular meetings and special meetings. Violation of the laws carries a fine up to $500 or a jail term up to 10 days.