Braden began shouting at the chief about the city's crime woes at Wednesday's rally. At one point, Chief Eric Jones told Braden he would be escorted out if he didn't wait his turn to speak.
Stockton filed for bankruptcy earlier this year and has experienced a surge in homicides.
Braden later told CBS-13 he was recently attacked in his car, and his grandmother was robbed. He has put his house up for sale, he said.
"Arm yourself or get out," Braden said. "It's the Wild West. The boys in blue, they're outgunned."
Braden said he brought the bat to protect himself.
A's spokesman Bob Rose told the Oakland Tribune the team had no comment and Braden would not be in trouble.
Braden has been sidelined following shoulder surgery.