Statements from eyewitnesses, text messages and video and physical evidence established that Baggett didn't violate any policy or procedure, Yates said.
"Based upon these facts and circumstances I made the decision to return them to active duty status," Yates said in an email.
Police said an investigation into Carter's death and drug-trafficking associated with the case is ongoing. The FBI has said it is monitoring the case.
Authorities said they presume Carter hid the gun in the back of the patrol car after the first pat-down, before he was handcuffed and searched again.
Police previously released video recorded from dashboard cameras the night of the shooting, but the footage didn't appear to show when officers found Carter slumped over and bleeding in the backseat of a patrol car as described in a police report.
Authorities said there were problems with the audio and video that explain the absence of a gunshot or noise on the recordings, though the lawyer for Carter's family hasn't accepted that explanation.