When you prepare your OH return you are given the option to complete your RITA form, but TurboTax never files it for you. The RITA form has to be printed, signed and mailed. If you did not do that then you did not file RITA. And you should have noticed that the payment was not made if you did not see activity in your bank/credit account to take out your payment. It is easier to use the RITA site to take care of your RITA tax than to use TurboTax. Sounds like you need to pay your 2017 RITA. (plus any penalty they are charging)
Then check and see what you did (or did not do) for 2018 if you still live in the same place.
You had to print and mail the RITA municipality return, it cannot be e-filed
See this TurboTax support FAQ for supported city returns - https://ttlc.intuit.com/community/returns-and-forms/help/which-city-tax-returns-can-i-do-in-the-turbotax-state-program/01/25578
See this Ohio RITA website - https://www.ritaohio.com/Individuals/Home/SubpoenaNotice
To access your current or prior year online tax returns sign onto the TurboTax website with the userID you used to create the account - https://myturbotax.intuit.com/
Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show. Click on the Year and Click on Download/print return (PDF)
I went to the ritaohio sight and created an account and put in my W2 for 2017. By the looks of my W2 they took KY city taxes for the city I work in and Ohio state taxes. I live in Ohio but work in Ky.