How can I file my state tax without the federal tax? I have already filed my federal tax on the IRS website but am unable to file my state tax there.

No.

 When you use TurboTax the information flows from the federal return to the state return.  You cannot use TT to prepare a "stand alone" state return.  Try going to your state's tax website to see if you can file there.

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/0...

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 pay for state and mail the state return.
https://ttlc.intuit.com/community/filing-and-paying-taxes/help/can-i-prepare-and-file-just-my-state-return-using-turbotax/00/26408