A connecting device includes a connecting member having a primary flow channel and secondary flow channels, each provided with a proximal aperture intended to be fluidically connected to a respective tube for medical treatment fluid administration and with a distal aperture, the distal aperture of the primary flow channel being positioned between the distal apertures of the secondary flow channels, and a connection endpiece intended to be connected to a catheter, the connection endpiece having a mounting portion in which the connecting member is mounted, the connecting member and the connection endpiece delimiting an internal chamber into which open the distal apertures of the primary and secondary flow channels, where the cross-section of the distal aperture of the primary flow channel is greater than the cross-section of the proximal aperture of the primary flow channel.