Get your taxes done using TurboTax

Since you have information recorded in Boxes 15-17, you will need to file a NJ non-resident return to declare the income was earned in another state. Since you mention Box 17 is filled out, you should receive a refund to taxes paid in NJ. Prepare your NJ non-resident return first, to receive your refund and then prepare your Connecticut state return. 

As you prepare your NJ non-resident, it will ask if you earned all your wages in NJ, here you will say you earned some of the wages in NJ and then put 0 for the wages earned in NJ. If you get an error message at the end, you can print your NJ and mail it in accordance to the mailing instructions given.

Here is the screen where you will make the choice to declare your NJ wages non-taxable.