It depends. On your W2 from the company was there a line on your W2 with box 15 "NJ" and boxes 16 and 17 in that NJ line showing income and income taxes withheld by NJ. If not, there is no need to file a return as there was no income tax withheld. I surmise there are no NJ items on your W2 or TurboTax would have asked you to complete a NJ return originally.
The items you list as being withheld are insurance items (short-term disability, unemployment, Family Leave). If for some reason you needed to use any of these and you had not paid into them you would not be eligible to receive any benefits. That's why they are being withheld. These items are not refundable.
If however, you do have NJ boxes on your W2, then you would need to file a NJ non-resident return to claim the income tax withholding refund. In TurboTax at sign in select the "Add a state" option to allow you to make changes. In the "My Info" section scroll down to "Other state income" and "Edit" to answer "Yes" you earned money in another state and select "NJ".
Next verify your W2 entries in the "Income" tab include the NJ boxes 15-17. Finally select "State" in the left hand menu and then "Prepare State Returns" and "Start" your NJ return.
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