Live/work in Califronia, but also received W-2 from Ohio

1. Yes, OH requires nonresident with Ohio income to file unless you have $0 taxable income.  Your income is below the threshold so you do not need to file a return. You can file a return to get your state tax paid back.

See Ohio - Ohio Filing Requirements . You may need to file a local return. Ohio has city returns and school district returns so the rules and filing vary. If you want to reply with the location, we can see what you need to do.

2. CA is your resident state and does tax all income earned. If you do have a state tax liability for OH, then CA will give you a credit for the double taxed income. 

You get credit for the lower state tax on the lowest taxable amount.

• Each state calculates taxable income differently. 
• Each state has its own tax rate/ system.
• You get the lowest of both categories as a tax credit.