No, since this is a NY S-corp, do not check the box for "non-electing S-Corp." But do include the S-Corp income on your NJ tax return.
Be sure to prepare your non-resident New York return first. This allows TurboTax to transfer the NY information correctly to your New Jersey return.
If you've already started your NJ return, go to the States topic and delete that state. Then review NY before you add NJ to your return.
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