No you cannot. When you use TurboTax the information flows from the federal return to the state return. You say you already filed a federal return using a different software program. You will not be able to file a federal return using TurboTax nor will you be able to e-file a state return. TurboTax cannot be used to prepare a stand alone state return.
You could go on your state's tax web site to prepare and file the state or get the state forms to prepare and mail.
https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573
You will need information from the federal return you filed.