Withdrawals from a traditional IRA are usually not fully taxable in New Jersey. But any amount that would be taxable if you simply withdrew it from the IRA is also taxable if you convert it to a Roth IRA. For more details see the following publications from the New Jersey Division of Taxation.
Tax Topic Bulletin GIT-2, IRA Withdrawals
http://www.state.nj.us/treasury/taxation/pdf/pubs/tgi-ee/git2.pdf
Technical Bulletin TB-44(R), Roth IRAs
http://www.state.nj.us/treasury/taxation/pdf/pubs/tb/tb44.pdf
Publication GIT-2 has not been updated for 2018. The exclusion amounts will be higher for 2018, and the line numbers on Form NJ-1040 may change, but the rules are otherwise the same.
