What do I do to throw away pieces of wood, branches, twigs, etc?

I had a dead tree. I broke off branches and twigs. Some were big, others small. I'm not sure if I'll be fined for just placing them in a black garbage bag and leaving it out for the garbage trucks to take. What should I do? Do I tie up the bigger pieces (if so, how big) and leave the smaller ones in a black bag?