City Council President Ernest Congo said the community is demanding clarity about what happened.
"The family deserves answers. The community deserves transparency. This investigation must be thorough and independent," he said.
Wilmington police reported that Skinner was shot and killed by an officer on June 24 near 24th and Jessup streets.
RELATED | 'We need answers': Family disputes details after man killed in Wilmington police shooting
Family disputes details after man killed in Wilmington police shooting
According to the department, detectives determined that officers saw Skinner point a firearm toward a crowd before running away.
Police said an officer chased Skinner and shot him in the buttocks. He was taken to a hospital, where he was pronounced dead.
On Wednesday, Mayor John Carney and Police Chief Wilfredo Campos issued a statement saying the department had offered Skinner's family an opportunity to view the body-worn camera footage.
"As a follow-up to the June 25th meeting that previously took place between family members and Chief Wilfredo Campos, WPD extended an offer for the family to see the body-worn camera footage. The offer remains open for them to accept at any time they are ready," the statement read.
The shooting remains under investigation by the Wilmington Police Department and the Delaware Department of Justice.
Skinner's family and local leaders have questioned why he was shot in the back.
Council Member Coby Owens urged unity and transparency.
"Let's stand together as a community. Let's make sure we get justice for Mr. Skinner. A young teenager shot in the back. Let's make sure the body-worn camera is released," he said.
Police said they recovered Skinner's handgun at the scene along with ballistic evidence, which has been sent to forensic technicians for analysis. The officer involved has been placed on administrative leave.
Skinner's family declined to comment when contacted, but they will be alongside their attorney, Ben Crump, at a press conference scheduled for Thursday at 9 a.m.