No. Causality is all you need to identify who the criminal is.
Physical stimuli are basically all we need as intelligent beings to come to a conclusion about things we don't like happening to us, and thus ultimately make into moral laws or codified ones. These are the inputs, these are the causes. Then, once enough human beings have had those inputs result in a large enough collective coming to the conclusion that stuff is Bad, we end up with laws.
Then, whenever someone acts in a way that we have determined is Bad, they are the criminal. They do not need to possess free will for the rational thing to do to be to provide punishment for them, because punishing them ultimately changes the inputs used by others to reach decisions. Nothing about this requires free will - it's all just as applicable if you just believe the laws of physics and causality determine every choice we make.