Officers shot 37-year-old John Penny in the leg and forearm on Aug. 14, near Thornton Court and Pacific Avenue, the LAPD said.
The incident began as a police response to reports of a screaming man.
According to investigators, the shooting occurred after Penny picked up the wooden plank and moved toward the officers, ignoring their repeated commands to put it down.
Penny, who was on probation for battery at the time of the incident, subsequently surrendered and was taken into custody.
The Los Angeles County District Attorney's Office later charged him with three counts of preventing an executive officer from the performance of their duties, and one count of possession of a dangerous weapon.