NY state requires an electronic return. Turbo Tax is making me file by mail. How do I get an electronic return? Do I need a refund from Turbo Tax?

You can e-file if you e-filed your federal return.   Did you e-file your federal return?   If you did not e-file your federal return, you can't e-file your state return(s).   

Is there another reason it is showing as to why you can't e-file?   If TurboTax can't e-file your return, NYS will exempt you from the e-file requirement.   You're required to electronically file your return if you meet all three of the following conditions:

• you use software to prepare your own personal income tax return; and
• your software supports the electronic filing of your return****; and
• you have broadband Internet access.

If the software doesn't support e-filing your return, you are not required to e-file your NY return.   See here.