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Mrs. Dixon said the police commissioner’s job is a 24-hour-a-day, seven-day-a-week job that takes “priority over family, friends and everything else.”

Mr. McCarthy said there was “a perception and a reality about the energy level at the top of the police department and the energy level committed to communicating the policy.”

“At the end of the day, I have to tell you it was about leadership,” Mr. McCarthy said.

“The mayor needed a strong energetic leader to implement a public safety strategy that when she is in the community, she hears is working.”