The arrangement for connection of a medical device, particularly a dialysis device, to a permeate line for the supply of permeate into the device is characterized by an adapter comprising a first supply line section with a terminal coupling member for connection to the water line, a pressure sensor and two successively arranged shut-off valves, and two second supply line sections that branch off from the first supply line member by means of a branching member. Both second supply line sections are connected to two different lines of the device in such a manner that disinfection fluid flows through both second supply line sections in a disinfection process of the device.