No, you do not need to file for the State of the payer registration if you never lived or work there.

You can enter the 1099-Misc in TurboTax using the following steps:

1. Click on Federal Taxes > Wages & Income. [In TT Home & Biz:  Personal > Personal Income > I'll choose what I work on.]
2. Scroll down to the 1099-Misc and Other Common Income section. 
3. Click on the Start/Revisit box next to Income from Form 1099-MISC.  (See Screenshot #1, below.)
4. On the screen Did you get a 1099-Misc?  click on the Yes button. (Screenshot #2)
5. Enter the information from the 1099-MISC.
6. On the screen Does one of these uncommon situations apply? mark that This was prize winnings and click Contnue.  (Screenshot #3)
   
7. Continue through the rest of the interview screens.

The income will appear on line 21 of form 1040 (Other Income).