Though laws regarding slavery varied from state to state, the answer is that slaveholders were not criminally liable for their enslaved property but were subjected to limited civil liability. Enslaved property is treated like any other significant property, such as a horse or land. If harm resulted from your negligent use of that property than a lawsuit was warranted. As for criminal law, enslaved people were tried in the regular courts but generally through a much more attenuated criminal process. If they were convicted of capital crimes they were executed and their owners would receive a significant portion of their value from the state treasury.