A connector device is disclosed which can branch or terminate signal lines for making a mutual connection among a plurality of units. The connector device includes switches between signal line connection terminals so that the connector may serve as both a branch connector and a strap connector. A hook is provided on a body case of the connector device and usable in interlock with the switch. A groove engageable with the hook is formed on a connector element case for external circuit connection so that through the selective engagement of the hook with the groove the element case is prevented from being inadvertently detached from the body case. During the detachment of the element case, the contact pin is placed in a short-circuited state at all times. A terminating connector device is also disclosed which is comprised of a combination of a connector body with first and second connector elements. The connector body includes first and second pairs of terminal. The first connector element has two terminals detachably connected to the corresponding terminals in the first pair and second connector element has two terminals detachably connected to the terminals in the second pair. A terminating resistor is inserted between the two terminals of the first elements. An additional connector element is prepared which is of the same type as the second connector element with no such terminating resistor. The additional connector element is matingly connected to the connector body in place of the connector element with the terminating resistor, thereby providing a branch connector.