A video indicates that Polk was holding a hatchet over his head in a threatening manner when he was shot by the officer Saturday night, police spokesman Jeff Thomason said.
Thomason said Polk's death could have been avoided if he had "listened to the officer and put down his hatchet."
The hatchet that Polk was wielding was 12 inches long.
Thomason said the female officer, who's been a member of the department for 18 months, "gave instructions and commands to Mr. Polk but he didn't respond to them and advanced" toward her.
The owner of Tolin Liquor Store at 7101 International Blvd. called police shortly after 9 p.m. Saturday to report that Polk, a 46-year-old Oakland man, was causing problems inside the store by harassing the owner and store customers, Thomason said.
Before officers could respond, the owner then flagged down the woman officer, who was driving in the area, according to Thomason.
He said the officer apparently chose to shoot Polk instead of using a Taser or pepper spray because he was inside a threshold area where a suspect can kill an officer if they have a stabbing instrument.
Thomason said pepper spray is "ineffective" in stopping suspects who have stabbing instruments at close range and Tasers also are often ineffective when officers deal with suspects who are at close range.
He said both prongs have to hit a suspect for a Taser to be effective and the bulky clothes that Polk was wearing may have prevented the prongs from going under his skin.
The female officer fired several rounds at Polk with her service pistol, according to Thomason.
Polk was then transported to Highland Hospital in Oakland, where he was pronounced dead.
The officer has been placed in paid administrative leave while the incident is being investigated by the Oakland Police Department and the Alameda County District Attorney's Office.
Investigators recovered a video from the liquor store's security system. Thomason said it corroborates the officer's version of the incident.
However, Polk's family issued a statement tonight, saying that Polk had a "peaceful spirit" and didn't threaten or harm anyone at the liquor store that evening. They said he frequented the store and was acquainted with all the clerks.
The family said he went to the store on Saturday to buy a pack of cigarettes.
"Then a series of events, still unclear, happened; tragically ending in his death," the statement reads.
"We are deeply saddened by the loss of our brother, father, uncle, son and friend. Brownie's death leaves his 16-year-old son, Brandon without parents. Brandon lost his mother to cancer six months ago," the statement reads.
Polk's family thanked the community for its support and urged residents to remain calm during the investigation into the shooting.
The incident was the fourth officer-involved shooting in Oakland this year. There were 10 officer-involved shootings in the city in 2008 and 11 such shootings in 2007, according to Thomason.
Bay City News contributed to this report.