It is difficult to prove a capable sufficient condition for the exact
controllability of systems containing nonlinearities and randomness. As
a result, scientists are investigating the concept of approximate
controllability for such systems. In this paper, we handle the so-called
C-controllability, which was suggested as a weaker analog of the exact
controllability at the beginning of the period when controllability
issue oversteps to stochastic systems. We prove a sufficient condition
of C-controllability for a semilinear stochastic system driven by a
Wiener process. This sufficient condition is verified on examples. Two
ways of improvement of this sufficient condition are discussed.