  In this note we are concerned with estimates for the spectral projection
operator $\mathcal{P}_\mu$ associated with the twisted Laplacian $L$. We
completely characterize the optimal bounds on the operator norm of
$\mathcal{P}_\mu$ from $L^p$ to $L^q$ when $1\le p\le 2\le q\le \infty$. As an
application, we obtain uniform resolvent estimate for $L$.
