A "duplex" describes a style of building rather than a form of ownership, so it depends. Since you are talking about Bath, I imagine it is one of the townhouses in the "Brick Project" off High St. or perhaps, the "double house" on Washington Street. In either case, the owner of the "house" owns the lot that the dwelling sits upon - it is not "common area" such as you would have with a condo. The deed tells you what you would be purchasing. You can investigate insurance coverages and costs with your insurance agent or company. And, you should consult an attorney with any concerns, or to get legal advice.