Agree with MA NR return and CA resident return, wage income included on both, credit for MA tax on CA return to prevent paying tax twice on the same income. If MA tax is higher you won’t get full credit back, as you can reduce CA tax to zero but not below zero. If CA tax rate is higher you may end up owing some CA tax after the credit. Net effective tax rate is the higher of the two rates.
Generally a full time OOS student is still a resident of the state where their parents still live.
This statement is wrong, or at least not right. The OP’s child is taxable in her state of residence – California, no question about it – on income earned everywhere. She is taxable in Massachusetts as a nonresident on income she earns in Massachusetts (although her tax rate may be affected by income she earns elsewhere). She gets a credit on her California taxes for taxes she pays to Massachusetts on income that is taxable in California, up to the applicable California rate on that income. If the Massachusetts rate is the same or higher than the California rate, she won’t pay any California taxes on that income. If the Massachusetts rate is lower, she will pay California the difference between the Massachusetts rate and the California rate.