TMZ Sports broke the story ... Brown is being sued by a man who claims his 22-month-old son was walking around the pool area at the complex in April when vases and other items landed within feet of him.
The man says the items came from Brown's room -- and since the child is now suffering night-terrors and other emotional issues stemming from the incident -- he wants Brown to pay.
The owners of the apartment complex have also filed a lawsuit against Brown claiming he caused significant damage to his apartment.
But Brown just issued a statement saying, "It has now been made public that two lawsuits containing false claims have been filed against me.