It comes down to the question of criminal capacity, which is the term for a person’s ability to understand that the action is wrong / unlawful and that there are consequences attached.
If a 3-year-old knows about guns and says he wants to shoot someone, he knows it is wrong but cannot be presumed to understand the consequences attached. With that said, the child would be evaluated to determine their ability to understand the situation, as well as what the appropriate consequence can be.
This also raises the 2 stages of the criminal sanction. Step 1 is conviction and step 2 is sentencing. Even if a 3-year-old can be found guilty of murder, the child can’t be sent to prison and probably can’t even be sent to a juvenile facility. Most likely, there will be a series of psych interventions to alter the child’s home circumstances.
In addition to this, the adult(s) in charge of this child will be looked at for culpable homicide (manslaughter) charges, as well as possible child endangerment (if the child had access fo a weapon).
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