When will I get my Ohio state tax? I already got my federal but no state yet

The Federal and State refund process is completely separate. The Ohio Department of Taxation states that: Taxpayers who request a direct deposit for an original return may expect a refund within 15 business days (it can take longer). Paper returns will take approximately 8 to 10 weeks to process. 

If the refund is not received in this time period, please use the “Check My Refund Status” option on the tax.ohio.gov website using the following URL: https://www.tax.state.oh.us/IFILE/WheresMyRefundWeb/wheresmyrefund.jsp

For refund related questions: Contact a representative at 1-800-282-1780 or E-mail Us.

I still haven't received my federal or state refund and I received an email on March 4th stating it would deposit with in 1 to 3 business days.

For your federal refund, once the IRS Where’s My Federal Refund? site shows "Refund Sent" it can take 1 to 5 business days for the financial institution to deposit fund into your account. The email you received may have been from TurboTax with the estimated timeframe based on the IRS's 21 day timeframe but some returns take more time to review. For the most up to date and accurate information regarding your refund visit the IRS website Where’s My Federal Refund?

The general timeline of e-filed returns is: Transmission > Acceptance > Processing > Approval > Refund.

Please see the link below for more information:

When will I get my IRS tax refund?

The State refund is processed by your individual state, so it depends on when they process and complete it. 

You can track the status of your state return by following the directions in the following TurboTax FAQ.

How do I track my state refund?