E-file only NJ State Tax

You can't use Turbo Tax for that.  Maybe you can directly on the NJ website.  Why can't your tax preparer do your state return?

You cannot do what you are asking for with TurboTax. The state tax return is based on the federal return. You would have to first recreate your federal tax return in TurboTax, making sure that it exactly matches the return that your tax preparer filed. Then you could prepare your New Jersey nonresident return.

With TurboTax Online you cannot fill in the forms directly. Everything has to be entered through the question-and-answer interview. If you purchase the CD/Download TurboTax software that you install on your computer, theoretically you could complete your federal and state tax returns in forms mode. But that is complicated and error-prone, and cancels the TurboTax accuracy guarantee. Furthermore, you can't just make entries directly on the forms that get filed. Most information has to be entered on supporting forms and worksheets, from which it flows to the filed forms. The state software cannot run by itself. You would have to purchase both the federal and state software. If you purchase the Deluxe or higher edition it includes one state program. And finally, you cannot e-file a state tax return in TurboTax unless you have e-filed your federal tax return with TurboTax.

You might be better off just downloading the blank forms from the New Jersey Division of Taxation web site, filling them out by hand, and filing by mail.

Why do you have to file your New Jersey nonresident tax return by yourself? The simplest solution by far would be to have the tax preparer who filed your federal return do the New Jersey return.