The connector for a fluid line of an extracorporeal circuit comprises a tubular body which internally defines a fluid passage, a first connection port predisposed for coupling to the fluid line, a second connection port predisposed for coupling to a male Luer connector borne by an external element, and a closure element of the second connection port. The closure element is formed of a breakable membrane made in a single piece with the tubular body. On coupling, the membrane is broken by the truncoconical projection of the male Luer connector. The connector connects a service line of an extracorporeal circuit to a pressure sensor of a dialysis machine.
