Ryan O'Neill's resignation took effect immediately, said Ruszkowski.
"I'm getting his letter of resignation, I will not have any comment for now," Ruszkowski said.
Police said O'Neill shot Eric Jack Logan on June 16 as Logan entered a car with a knife in his hand.
The shooting hit the community of Indiana, highlighting years of racial tension between the South Bend Police Department and the African-American residents of the city.
Shirley Newbill told Buttigieg that she "has spent my entire life here" and that the authorities have not done anything about me or my son, nor that any of these people are find here.
Buttigieg has largely put its campaign on hold to remedy the situation.