Work in Cincinnati and Live in KY. Do I need to file Cincinnati taxes? Have just one W2 from my employer and have KY in my W2. I already filed my taxes. What to do?

I just finished filing my taxes using Turbotax paid products. I filed for federal and KY. I live in KY (Florence) and work in OH (Cincinnati). I do not understand if I need to file for Cincinnati and even if this would mean to pay extra taxes. My only income is from just one employer (big corporate in Cincinnati). I do have just one W2 but none of the boxes are filed with Cincinnati taxes. What should I do?