(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.
The Mekhilta Asks Does This Mean the Master Is Liable Regardless
Mekhilta Tractate Nezikin 7:7