Here's an excerpt the NJ Courts website:
The security deposit generally must be deposited in an interest-bearing account in a bank or saving and loan association in New Jersey at the time the lease is signed. The landlord must give written notice of where the money has been deposited within 30 days of receipt by the landlord.
If the landlord does not return the security deposit within 30 days from the date the tenant moves out of the premises, the tenant may sue to recover double the amount due, plus court costs. If the amount sought is $3,000.00 or less, the tenant may sue in the Small Claims Section. If the amount sought does not exceed $15,000.00, the tenant may sue in the Special Civil Part. If the amount sought exceeds $15,000.00, the tenant must sue in the Law Division.
The landlord must notify the tenant of the amount of the security deposit being retained and the nature and cost of the repairs.
If the amount of any damage caused by a tenant plus any unpaid rent is more than the security deposit, the landlord may sue for the additional money.
If a residential building is sold, the seller must turn over each security deposit plus any interest to the buyer and notify each tenant by registered or certified mail.
If the landlord doesn't put the money into an interest-bearing account, the tenant may give written notice to that person that such security money plus an amount representing interest at the rate of seven percent per annum be applied on account of rent payment or payments due or to become due from the tenant, and thereafter the tenant shall be without obligation to make any further security deposit and the person receiving the money so deposited shall not be entitled to make further demand for a security deposit.
http://www.state.nj.us/dca/divisions/codes/publications/pdf_lti/sdepsit_law.pdf (see p. 2).