If you have small lottery winnings that you paid state taxes on but not enough to pay federal then how do you claim it on your state taxes so I can get my state return? Can anybody please help me? Tha

When you use TurboTax the information flows from your federal return to the state return.  So prepare both returns to let the information go on to the state form.   You cannot prepare a "stand alone" state tax return using this software.

If you qualify to use it, there is another full-featured free version of the software:

Try Free File: 

You qualify if your income was $39,000 or less, or $72,000 or less if active duty military, or if you qualify for Earned Income Credit

https://ttlc.intuit.com/questions/1900583-what-is-turbotax-free-file-program

• https://ttlc.intuit.com/questions/2026912-how-do-i-switch-to-turbotax-free-file-program

Note:  If you do not qualify to use Free File then you will have to upgrade to Deluxe or higher in the paid versions of the software.   

Online Deluxe $40  State software $40

there is no such thing as lottery winnings too small to pay Federal taxes on. your winnings must be entered on the federal return and then they will flow to the state return.