Can I file state tax separately at turbo tax?

How did you file federal?

If you didn't use Turbo Tax to do your federal return, you would first have to fill out a federal return (don't file it) to match the real return you did file and you would have to pay for federal for it to flow into the state return. Then you would have to mail the state.
https://ttlc.intuit.com/community/filing-and-paying-taxes/help/can-i-prepare-and-file-just-my-state-return-using-turbotax/00/26408

I'm not sure what you mean by "separately." If you already filed your federal tax return somewhere else, the best way to file your state tax return is by the same method you used for the federal tax return. The state tax return is based on the federal tax return. If you use the same method that you used for your federal tax return, the federal return is already there. In order to prepare a state tax return in TurboTax, you first have to have your federal tax return in TurboTax. If you filed federal elsewhere, you would have to recreate your federal tax return in TurboTax, and make sure the it exactly matches the federal tax return that you filed.

You cannot e-file a state tax return in TurboTax Online unless you e-filed your federal tax return with the same TurboTax Online account. You could print your state tax return and file it by mail.