Connector for a fluid transport line of a medical device, comprising: a first body (2) having a first access port (3) for a fluid, a second access port (4) for a fluid, and a first fluid path (5) extending in the first body (2) and directly connecting, for fluid transport, the first access port (3) and second access port (4), at least a second body (6), mountable to the first body (2), having at least a third access port (7) for a fluid, the second body (6) being movable with respect to the first body (2) at least between: a main operating position in which the first fluid path (5) is interrupted and in which a second fluid path (9) is defined and enabled, for fluid transport, from the first access port (3) to the third access port (7), and an auxiliary operating position in which the first fluid path (5) is enabled and in which the second fluid path (9) is interrupted. The second body (6) has at least a fourth access port (8) for a fluid and in the main operating position a third fluid path is defined and enabled, for fluid transport, from the second access port (4) to the fourth access port (8), the third fluid path being interrupted in the auxiliary operating position.
