New Jersy does not have an itemized or standard deduction. However, they do have some things you can deduct. It makes no difference on the New Jersey form if you took standard or itemized on the federal return. Your premiums can be a part of that.
From New Jersey:
https://www.state.nj.us/treasury/taxation/njit13.shtml
Federal deductions, such as mortgage interest, employee business expenses, and IRA and Keogh Plan contributions are not allowed on the New Jersey tax return.
You can deduct certain medical expenses that you paid during the year for yourself, your spouse or domestic partner, and your dependents. However, you cannot deduct expenses for which you were reimbursed. Only expenses that exceed 2% of your income can be deducted.
If you look at the screenshot, you can see the other deductions. There is a page in TurboTax asking about these, including the medical deduction. See screenshot.