His brother told reporters Friday that the officer had set his gun down on a table, and then accidentally knocked it to the floor when he returned to the room.
The gun discharged, firing a bullet that passed into the apartment below and hit 1½-year-old Jonathan Porcellini in the arm.
The lights were off because the pair, who are roommates, couldn't pay their bills, the brother said. The Police Department said Venetek makes about $34,000 per year. In New York, many families pay that much annually in rent.
The injured child was treated at a hospital and released. The wound was not life-threatening, but his family is still angry.
"Just a few more inches and I could have lost my son," said his father, Justin Porcellini. "This is a city employee, a cop. They are supposed to be safe. I want people to know that what happened was wrong."