Your son continues to be a resident of your state because college is considered a temporary absence. As such the scholarship income is taxable in your state under all circumstances.
You may need to do some research as to whether the scholarship is taxable in the state where your son is attending school, but it likely is considered as such. In that case, your son may need to file a nonresident state return to claim the scholarship income to that state, and a resident return for all of the income. If he must pay any taxes to the nonresident state, your state should give a credit for the tax you pay to the other state.
One exception could be if the two states have a reciprocal agreement. If they do, they may well accept the scholarship income (which are considered to be a type of wages) as falling under the reciprocal agreement and just reported to your state, the resident state.
If the state where your son is attending school is Alaska, Washington, Wyoming, Nevada, South Dakota, Texas, Florida, Tennessee, or New Hampshire, these are states that do not have a state income tax. The scholarship income would be taxed only in your state.
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