Technically, your son's tax home is where he has driver license and is registered to vote. Attending college in a state does not make your son a residence of that state. If you will claim him as your dependent, your son should be the primary resident of the state you live. For your case, your son will need to file both state since he may have withholding on his CA tax. He will file as non-resident for CA and full year resident for NY where is his home state return.
Here is other cases that is similar to your son's case for your reference.
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