refer to New Jersey landlord laws to see what the requirements are
@Cathy M. These articles appear to answer your question:
@Kyle J. 2 great articles, thanks! That does clear it up. I will need to put the security deposit in a bank that has branches both in Florida and New Jersey. That is what I thought.
I had to travel up to New Jersey before my tenants moved in anyway, so I just deposited their check in my NJ bank in a tenant account.