Shoemaker said "the way the situation transpired wasn't optimal."
Frazier alleged that county paralegal Lyn Mallick, who was relieved of her duties July 18, was let go as a "political firing to suppress the minority opinion," referring to herself and Commissioner Richard Rothschild.
Frazier said she was not involved in any discussions to terminate Mallick's employment.
Rothschild agreed with Frazier, calling the move an "abuse of power."
"It is inappropriate for three commissioners to remove support personnel from a fourth commissioner without their knowledge," he said.
Frazier hired Mallick as a part-time researcher and analyst in January and said her position is included in the budget passed by the commissioners. Each commissioner has the opportunity to hire a part-time assistant when elected.
Howard said this position was created and filled in January without his or Roush's knowledge. He alleged Frazier secretly obtained the signatures of three commissioners to create the position.
Although Frazier blamed Howard as the commissioner behind the firing, Howard said the decision was made by the majority of the board.
"I do not make personnel decisions based on politics," he said. "I make them based on performance and the best interests of Carroll County."
Frazier said she intends to seek Mallick's reinstatement instead of hiring someone else for the position.
She proposed that commissioners publicly discuss reinstating Mallick at the board's Aug. 1 meeting, but could not get enough support to put it on the agenda. The board is instead expected to discuss its hiring policies and procedures.