If I moved from Colorado to Ohio the middle of December of 2018 and never worked in Ohio, why am I having to fill out Ohio taxes?

[jlbisin]

If I lived in Colorado school district for majority of the year, and have moved to Ohio,do I fill in the district number for current Ohio address?

[Hal_Al]

You told TurboTax that you moved, so it recognizes that you lived in two states. 

As a part year resident of Oho, you are technically required to file a part year resident return, even if you had no income while a resident. If you had no income (e.g. retirement check or interest and dividends), you will not  owe  Ohio any tax and can probably "get away with" not filing, for such a short time. 

I you do not file an Ohio return, you should file a full year resident CO return.