I live and run my business in Ohio but an a resident of California as an active duty dependent.

Yes, as an active duty military spouse, you can maintain your California residency for tax purposes while living and running a business in Ohio. 

Your business in Ohio may be subject to Ohio taxes since the revenue is earned there. You will likely need to file a California resident return to report worldwide income and a nonresident Ohio return.

If you meant something else reach back out.

To File Multiple State Returns in TurboTax

1. Sign into TurboTax.
2. Click Complete the personal information section, identifying the state in which you live and answering questions related to military status.
3. When you get to the States section of Taxes, be sure to complete the nonresident tax return first to help ensure you receive appropriate credits. If your nonresident state is not included, automatically, follow the steps here.