But the mayor did not tell the public or the City Council why Mr. del Pozo was placed on leave until Dec. 13, when Seven Days, an alternative weekly, approached him about the tweets.

At the time, the mayor said doctors for Mr. del Pozo, who had been seriously hurt in a bicycle accident in 2018, confirmed he had an “underlying mental health issue” that had contributed to erratic behavior on the part of the chief. City councilors criticized the mayor, arguing he should have been more transparent with the public.

Mayor Weinberger said he was trying to preserve Mr. del Pozo’s privacy.

“Our city employment professionals strongly advised that we should treat the chief like we would treat any other employee and protect his medical information,” he said in an interview. “It was a challenging decision but that’s the way we chose to handle it and I stand by that decision.”

On Dec. 16, Mr. del Pozo submitted his resignation letter.

“It became clear by the end of that weekend that he was going to face continued criticism and that the path forward for him to remain in the position was going to be very challenging,” Mayor Weinberger said.

The mayor then appointed Jannine Wright, the deputy chief, to succeed Mr. del Pozo.

But soon after her appointment, Ms. Wright told the mayor that she had created two fake Facebook accounts, one under the name “Lori Spicer” and the other “Abby Sykes.” She was demoted back to deputy chief the same day, and later put on administrative leave.

The accounts went after Mr. Winkleman and city councilors, including Mr. Tracy, who were critical of the department following the death of a man who was punched during a confrontation with a Burlington police officer last March.

“You have publicly convicted an officer of murder when he has not had due process,” said one post written in June 2019, according to the findings of an internal police investigation. “Shame on you.”