Can we refuse to connect a sewage line that is on our property? Can we be sued?

Most likely not. In that chances that there is an easement which allows the connection even-do it is on your land. In essence if you replace the line and block there connection and it backup into there property you may be liable for damages.

Most municipalities have laws that require that any discharges be connected to their system, but that is not your real issue. You need to take all your title information to a real estate lawyer to see what rights, if any, your neighbor has to connect to your line. If you are putting in a new sewer line and your neighbor has some sort of easement, maybe you can leave him on the existing line and put in the new line just for yorurself.