The Orange County Sheriff's Office spelled out the allegations in new court documents, obtained by TMZ Sports, saying the killing happened a short time after Payne had arrived at Lawrence Dority's home in Orlando on Sunday night/early Monday morning.

According to the documents, a witness told cops she believed Payne had pulled up to the house to possibly play "mediator" between Dority and his girlfriend, who the witness said, "have a relationship where they argue often."

Cops say witnesses told them 29-year-old Dority ended up confronting Payne outside of the home when he arrived a short time after Payne got there.

In the docs, cops say Dority told them Payne "had no business being at his residence this late at night." Cops say Dority added that he took the former NBA player's "presence as a threat."

Police say Dority told them at one point during his conversation with Payne, the 6-foot-10 basketball player made "movements with his right hand in the right side of his waistband." Cops say Dority told them Payne then said "I'll smoke you bra."

According to cops, Dority immediately went into his home, grabbed a firearm, went back outside, and fired one round at Payne, before he returned to his residence. Cops say Dority said he was "protecting his family and protecting his home" -- and added that "his actions were justified."

In the docs, cops say 31-year-old Payne was struck by the gunfire and was later transported to a local hospital, but died there from his injuries.

Officers say following their immediate investigation -- which included interviews with witnesses and a review of surveillance footage -- they determined Payne was "not threatening Dority in any way." They said he had no firearm in his possession, and claimed Dority's "act was a premeditated killing."