Officially, Fishers Island belongs to the State of New York. It's shortest distance to the mainland however is with Rhode Island. It has a Connecticut zip-code, an east end of Long Island area-code, and views of Block Island. To reach the island, one must take a ferry from New London (there is a small airport too).
Most of Fishers Island is private and residential. As you may have already guessed, it is also very expensive. Much of the work that takes place here is performed by off-island residents. The girl at the pharmacy, the landscaper, and the electrician are often residents of southeastern Connecticut who commute here daily. That's where Baby Doll comes in.
Along with one other boat that I am aware of, Baby Doll departs Noank twice each morning and ferries workers to West Harbor on Fishers Island. In the afternoon, she does it all again and returns them home.
Sure beats the Cross Bronx Expressway!