A blood line connector for a blood circuit of a hemodialysis unit with an ability to make two different types of fluid tight connections, e.g., a screw-type connection with a luer connector at a patient access and a press-in type connection with a dialysate circuit. The blood line connector may include a tube connection end arranged to sealingly engage with a blood circuit tube, and a patient access connection end with a frustoconical member having an internally threaded portion arranged to engage with an externally threaded patient access, and a pair of locking arms extending rearwardly from the frustoconical member. The locking arms may each have a finger depression portion and a barbed portion, and may be arranged to engage with a mating connector on the dialysis unit at the barbed portions to lock the frustoconical member in sealing engagement with the mating connector when making a press-in type connection.