May or may not be relevant. Statistically, people with illnesses like schizophrenia are no more likely to commit violent crimes than the general population (but are more likely to be victims of violent crimes). There are documented cases of people with schizophrenia killing or commiting other violent acts in response to delusions, but it’s usually in an act that they perceive as self-defense rather than being driven by malice or desire to harm. I.e., it’s generally more like “I killed my dad because he was going to kill me” rather than “I went out and murdered some random women because no women like me.”