The woman told Dana Loesch's radio show that she heard Wilson's version of the events from his significant other on Sunday night.
The caller said that Wilson drove up alongside Brown and his friends and told them to get out of the middle of the street.
"They refused to and were yelling back," the caller said. "There was some cussing involved."
Wilson then apparently pulled over and the caller said she believes he then called for backup, but she wasn't sure. He then got word of the "strong arm robbery," and thought he saw what could have been cigars in Brown's hands.
Wilson then went back toward Brown, according to the caller.
"He goes in reverse back to them, tried to get out of his car. They slam his door shut violently. I think he said Michael did," she said.
When Wilson tried to get out of his car again, "Michael just bum rushes him, just shoves him back into his car, punches him in the face," the caller said.
Wilson then apparently went for his gun.
"Michael grabs the gun," the caller said. "At one point, he’s got the gun totally turned against his hip, and Darren shoves it away, and the gun goes off."
The caller said that Brown and his friends then "took off." Wilson yelled at them to "freeze."
Brown began taunting Wilson, yelling, "Oh what are you going to do about it. You’re not going to shoot me," according to the caller.
"He started coming at him full speed, and so he just started shooting. And he just kept coming," she said, adding that Wilson thought Brown "was on something."
"The final shot was in the forehead," the caller said, "and then he fell about two or three feet in front of the officer."
Listen to the audio, courtesy of The Dana Show: