  We show that if the presently observed L/E-flatness of the electron-like
event ratio in the Super-Kamiokande atmospheric neutrino data is confirmed then
the indicated ratio must be {\em unity}. Further, it is found that once CP is
violated the exact L/E flatness implies: (a) The CP-violating phase, in the
standard parameterization, is narrowed down to two possibilities pm pi/2, and
(b) The mixing between the second and the third generations must be maximal.
With these results at hand, we argue that a dedicated study of the L/E-flatness
of the electron-like event ratio by Super-Kamiokande can serve as an initial
investigatory probe of CP violation in the neutrino sector. The assumptions
under which these results hold are explicitly stated.
