  Let $\mathcal L$ denote the twisted Laplacian in $\mathbb C^d$. We study
almost everywhere convergence of the Bochner--Riesz mean $S^\delta_{t}(\mathcal
L) f$ of $f\in L^p(\mathbb C^d)$ as $t\to \infty$, which is an expansion of $f$
in the special Hermite functions. For $2\le p\le \infty$, we obtain the sharp
range of the summability indices $\delta$ for which the convergence of
$S^\delta_{t}(\mathcal L) f$ holds for all $f\in L^p(\mathbb C^d)$.
