My OH State Return says "Started" on My Tax Timeline, but I finished it the same time as I did my federal. I selected both get paid for from my federal return.

I also have that same thing. The response I received was that The state forms are not quite ready yet depending on your state. That once they are it should switch to completed. Hope that helps. 

Once your Federal return has been accepted, click on "Amend (change) Return". (You won't need to change anything). Click on "File" on the left hand side and progress through the prompts. You should now be able to file your State return.