Can i claim rent (for an apt in NJ) as deduction in NJ state return. Rent agreement has no mention of property tax but the owner must have been paying it.

Yes, you can claim the renter's credit if the apartment is a regular property and not a tax-exempt public housing that is handled by the government.

what section would that be located in

It depends. You would need to enter this in the New Jersey state return when you begin to work on it.

1. After logging into Turbo Tax, select state on the left portion of your screen.
2. You will navigate and enter answers in the interview.
3. Eventually you will reach an entry that says About the Homestead Rebate and Property Tax Deduction.
4. This is where you would start to enter the information.   

Just a bit of clarification here.

Can i claim rent (for an apt in NJ) as a deduction in JH state return.

Rent that you pay for your primary residence or any other non-business "personal use" real estate is never deductible on any tax return. However, many states that tax personal income do have provisions for and allow a "renter's credit" for a percentage of the rent you pay. If you are required to file a state tax return, then you will address this when you get to the state tax return. So that won't occur until you have completed the federal tax return and move on to the state return.

As a NJ renter, if your income is high enough, you enter 18%  of your rent on the property tax paid line.

turbotax should figure it correctly for you.