Which state? In general, state rules are similar to federal, but you need to be sure.
Q. Can my non-dependent claim the federal education tax credit for college tuition I as a parent paid?
A. Yes. For the federal credit, it does not matter who paid it.
But, there are other rules. There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
Generally, you cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return and he will not be eligible for a stimulus payment.
https://ttlc.intuit.com/questions/3936383-tuition-gift-to-children
https://ttlc.intuit.com/questions/4531097-just-because-i-can-claim-a-college-son-daughter-do-i-need-...
