Before I sign and file can I redo my state taxes for some reason I owe state I've never owned state taxes before

the only good reason not to e-file the state is because of the Turbotax fee.  you can change the state but if you already filed a version that was accepted you must do an amended state return. 

If you haven't filed yet

Go back thru your income areas in the Federal section, and make sure all your State wages and State withholding shown on W-2 (Boxes 15,16,17)  OR, the State withholding boxes on Other tax forms (commonly 1099-R, but could be other)  is properly entered.

Again, if you Have Not actually filed yet:

Yes, you can certainly navigate back to, and go thru all the State questions again to see if there are any special state deductions you missed, but most state $$ amounts (wages, other income, withholding, normal itemized deductions) are entered in the Federal section.