Can I just file the State taxes and not the federal?

It depends on the state, but in general you can do that.

You can only efile state if you first efiled federal from the same account or program and federal was accepted.  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