If you did a direct rollover from a 401(k) to an IRA, the 1099-R box 7 code will either be G (for traditional 401(k) to traditional IRA) or H (for Roth 401(k) to Roth IRA). If this is the case for your 1099-R, there should be a 0 or blank entry for box 2a. This would make it a non-taxable direct rollover.
Once you finish entering the 1099-R details in TurboTax, you'll get asked if you moved the money from a 401(k) to a Roth 401(k) - if this is clicked yes, the distribution will be taxable as a Roth conversion. If you didn't do that, be sure that you click No I didn't.
The next screen on Where is your distribution from? is to determine how it is handled for NJ purposes - this should be checked as None of the above because this is a rollover and not a distribution out of a retirement account.
You'll get asked if you moved the money to a Roth IRA - if your 1099-R was a traditional 401(k) and you click yes here, that will make the distribution taxable - click No if you moved the money to a traditional IRA.
Following the above steps will not make the 1099-R rollover distribution taxable in New Jersey.
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