  We consider a system of $N$ bosons in the limit $N \rightarrow \infty$,
interacting through singular potentials. For initial data exhibiting
Bose-Einstein condensation, the many-body time evolution is well approximated
through a quadratic fluctuation dynamics around a cubic non-linear
Schr\"odinger equation of the condensate wave function. We show that these
fluctuations satisfy a (multi-variate) central limit theorem.
