Women.
They talked among themselves. Maybe one of Fanucci's girls or his wife saw the murder but knew better than to say anything. But girls being girls, they talk and then it spreads through the streets.
I very much doubt it. If Fanucci's daughter had seen Vito killing her own father she would have likely said this to the police. At that point they did not need to fear Vito as he was still a nobody. It was only when the whole neighborhood knew he was the one who killed Fanucci that he was treated as a "man of respect", and this took a couple of weeks.
