Have been involved with several congs. over the years. While the method varies from state to state, the local group owns the Hall. In some states the local cong. forms a corporation which holds title to the Hall via that entity. Brooklyn does not own or have title. When loans are made Brooklyn holds the deed as a pledge against the debt. The deed is forwarded to the congregation once the loan is paid.
BTW interest is no longer charged on the loans the society makes. This stopped several years ago. At one time they charged 6% interest then dropped to 3%, then no interest. I think they got quite a bit of heat over charging interest on money that was donated for the express purpose of building halls.