  Let $F_N$ and $F$ be the empirical and limiting spectral distributions of an
$N\times N$ Wigner matrix. The Cram\'{e}r-von Mises (CvM) statistic is a
classical goodness-of-fit statistic that characterizes the distance between
$F_N$ and $F$ in $\ell^2$-norm. In this paper, we consider a mesoscopic
approximation of the CvM statistic for Wigner matrices, and derive its limiting
distribution. In the appendix, we also give the limiting distribution of the
CvM statistic (without approximation) for the toy model CUE.
