File a nonresident return with NJ to get any withholding refunded to you.
In TurboTax follow these steps:
1. Click My Info in left hand menu
2. Be sure your residence states do NOT include NJ.
3. Scroll down to "Other State Income", click Edit
4. Add NJ as a state that you earned income in.
Then
1. Click State in the left hand menu
2. Click Prepare State at top of page and Continue
3. Start New Jersey return
4. Be sure to zero out all income and deductions for NJ throughout the state interview.
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