מדרש אויף במדבר 35:18

(Exodus 21:20) "with a rod": I might think, whether or not it is of killing potential; it is, therefore, written (Numbers 35:38) "Or if with a wooden implement, whereby he can die he strike him," whereby we are apprised that he is not liable until he strikes him with something that has the potential to kill.

(Bamidbar 35:18) "Or if with a wooden hand-implement, whereby he can die, he strike him, and he die, he is a murderer." What is the intent of this? From (Shemot 21:20) "And if a man strike his (Canaanite) man-servant or maid-servant with a rod, and he die under his hand, vengeance (by the sword) shall be taken," I might think, whether or not it is of killing potential. It is, therefore, written "Or if with a wooden hand-implement, whereby he can die, he strike him, etc." — only if it is of killing potential. I might think, even on a (body) site injury to which does not result in death. It is, therefore, written (Devarim 19:11) "And if a man hate his neighbor and lie in wait for him, and he rise up against him and he strike him mortally," Scripture hereby apprising us that he is not liable unless he strikes him on a (body) site injury to which may result in death. This ("Or, if with a wooden implement") tells me that he is liable only if he struck him with wood. Whence do I derive (the same for) his throwing beams or poles at him? From "he is a murderer — die shall die the murderer" — in any event.