How do I file only state taxes and not federal?

If you are not e-filing the federal tax return then the state tax return can only be printed and mailed.  You will have to pay any TurboTax account fees before the tax return can be printed.

See this TurboTax support FAQ for the procedure to print a tax return for mailing using the online editions - https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online/01/26258

How did you complete your federal return?  Do you mean you just filed Federal already through Turbotax and did not finish the state forms. ? Turbotax pulls information from the federal return to start the state. Most many states require a federal form to be sent when you send your state return.   If you did the federal forms with another source you can go to your state tax website and print forms out.