Yes. And you can still claim the tuition credit or deduction, even though it was effectively her money that paid for the tuition, as long as she is still your dependent*.
You do not need her written permission, since the money was spent for her benefit. That is, the money doesn't have to be sent directly from the UTMA to the school. You are allowed to reimburse yourself for expenditures made on her behalf.
*UTMA money spent on support (including tuition) is considered support provided by the student, for the dependent support test.