A connector comprises a female connector housing having a flexibly deformable lock arm, a male connector housing having a lock portion elastically engageable with the lock arm when the two connector housings are completely engaged with each other, and a lock holding member rotatably mounted at an end of the lock arm. The lock holding member is selectively movable between an unlock position to allow the lock arm to be flexed in an unlocking direction thereof and a lock position to inhibit the lock arm to be flexed in the unlocking direction. In the complete engagement state, if a lock holding member in the end of the lock arm is rotated from an unlock position to a lock position, then the lock arm is prevented from being deformed flexibly to thereby be able to keep on the locking state of the connector. On the other hand, when the female and male connector housings are in incomplete engagement with each other, the lock arm is on the way to its flexible deformation. In this state, since the lock holding member is unable to advance into the flexing side of the lock arm, an operator can know that the female and male connector housings are in incomplete engagement with each other, in accordance with the fact that the lock holding member cannot be shifted to the lock position.