You will need to file a tax return for the state where your withholding was sent and a tax return for your resident state.
Since states do not share withholding with each other you cannot claim the withholding for one state on a different state's tax return. If you do not owe taxes to the state where your withhold was sent then you should get a refund of the taxes withheld. You will probably owe the state where your withholding should have been sent though since that state did not receive any taxes from your through the year.
Going forward you should talk with your employer immediately to get this fixed for 2017. If your employer has withheld state taxes during 2017 for the wrong state they may be able to correct it before the end of the year so you will only have to file one state tax return. If your employer cannot fix it in 2017, you will have to file two state returns next year also.