Let $\{X_{t}, t \in [0,1]\}$ be a Wiener process defined on $(\Omega, A, P)$ with covariance function $r(t,s) = E(X_{t}X_{s}) = inf\{ t, s\}$. We define the regularized process $X^{\varepsilon}_{t}= \varphi_{\varepsilon}*X_{t}$, with $\varphi_{\varepsilon}$ a kernel that approaches Dirac's delta function. We study the convergence of $$ Z_{\varepsilon}(f) = \varepsilon^{-\frac{1}{2}}{\displaystyle \int_{-\infty}^{+\infty}} [ \frac{N^{X^{\varepsilon}}(x)}{c(\epsilon)} - L_{X}(x) ] f(x) dx $$ when $\varepsilon$ goes to zero, with $N^{X^{\varepsilon}}(x)$ the number of crossings for $X^{\varepsilon}$ at level $x$ in $[0,1]$ and $L_{X}(x)$ the local time of X in $x$ on $[0,1]$.