I'm in the Army Reserves, and I live in KY. My Army W-2 still has OH listed as my state (box 15) because I forgot to update it when I moved from OH. How should I input?

You should input it as it was reported to you.

You can review your personal information in the My info section of the return to ensure your current state of residence is correct.

Kentucky and Ohio actually have state reciprocity. 

Check your W-2 form to see which state has the withholdings in boxes 15-17. 

If it shows Kentucky, you will only need to file a Kentucky return.

If the withholding is in Ohio, you will file the OH return since they have the income taxes paid into them already. 

This will result in your having 2 state tax returns, one for OH, and the other for KY.

I would prepare the Ohio return first as a nonresident. 

You will then prepare your Kentucky return.

When you prepare your Kentucky return, be sure to fill out the section indicating you paid taxes to another state in the credits section.

This will ensure you are not taxed on the same income twice.

If there is no OH withholding in box 17 of your W-2, you do not need to file an OH return.  

OH & KY do have a reciprocal agreement.  So. if OH tax was mistakenly withheld, you do need to file an OH  return to get it refunded.  KY will not give you a credit for tax  mistakenly paid to a reciprocal state (as one of the other replies indicates)