"I was livid," said Tammie Goodman, who is still waiting for justice in the 2018 abduction of her son Charleston outside their home off East Woodcroft Parkway.
Goodman said there's been a lack of communication with the chief's detectives and inadequate investigative work.
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Charleston Goodman's disappearance is now a cold case homicide investigation.
"Me hearing that he was shot in the head, then wrapped in plastic and fed to hogs. I mean, my granddaughter has to grow up one day and hear that, or go online and read that," Goodman said. "Just imagine. And she was only 5 years old.
"Chief Davis, I personally feel like you're running away from the problem instead of really trying to solve it," Goodman added.
Some speculate that Davis is job-hunting because of a lack of support from the city council on fighting crime. Davis has previously asked the board for money to hire additional officers and use ShotSpotter technology, a sensory device that detects gunfire.
Durham police chief C.J. Davis interviewing for Memphis police director job
"I think she has some great ideas, but she just wasn't allowed to produce those ideas," said Jackie Wagstaff of Durham.
Others said they think it is because of her national prominence; last year advocating on Capitol Hill for police reform as president of the National Organization of Black Law Enforcement, after the death of George Floyd.
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But there's concern that her potential departure could negatively impact minorities already suffering under the economic strain of COVID-19.
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"I respect her as a person who tries to do her best at her job. I don't believe in the institution of policing. It doesn't mean that I don't think Police Chief CJ Davis has done the best that she can in Durham. I do believe that," said Nia Wilson, co-director of Spirit House Inc.
In 2016, Davis was the first Black woman to become Durham's police chief. Combating violent crime has been a pervasive challenge with more recent shootings.
According to Durham Police, the city saw a 44 percent increase in aggravated assaults with a gun in 2020 compared to 2019.
Davis is one of eight candidates being considered for the director of police position in Memphis. The list was expanded to include Davis. The City of Durham said it is too early to speculate about her departure.
Officials offered these possibilities for the next steps if a new police chief is needed.
First, a deputy chief would be considered acting chief. A search committee would be hired and the three-to-four-month process for a permanent chief would include input from the community.
A source told ABC11 that Durham police staffers were surprised by the announcement.
ABC11 reached out to Chief Davis for comment and a response to Tammie Goodman's concerns but has not heard back.
The city referred ABC11 to the City of Memphis regarding its announcement Monday.