We broke the story ... the former Chicago Bulls star was arrested at a downtown L.A. apartment building after allegedly pulling a knife on the building manager, punching him in the face and demanding his security deposit back. He allegedly made off with a couple thousand dollars.

The case was kicked over to the L.A. City Attorney's Office which decided to move forward with 4 misdemeanor charges against Gordon -- battery, brandishing a weapon, criminal threats and carrying a knife in plain view.

We're told if he's convicted on all counts, he faces up to 3 years behind bars.