I am an Alaska resident going to school year round in California. My only income is from federal loans and the Alaska PFD. Do I file a state tax return for either state?

You don't have to file for California, but you should file for Alaska. With info given, you shouldn't owe any state income tax.

No, provided this is your situation: You have maintained bank accounts, voted, and filed your Federal income tax returns in Alaska during the entire period. You returned to your/ your parents' home (your principal domicile) for the summer and reentered California in September. Only paying non-resident tuition in CA is not enough proof to establish your primary domicile. Alaska has no income tax.