  On a relatively compact strictly pseudoconvex domain with smooth boundary in
a complex manifold of dimension $n$ we consider a Toeplitz operator $T_R$ with
symbol a Reeb-like vector field $R$ near the boundary. We show that the kernel
of a weighted spectral projection $\chi(k^{-1}T_R)$, where $\chi$ is a cut-off
function with compact support in the positive real line, is a semi-classical
Fourier integral operator with complex phase, hence admits a full asymptotic
expansion as $k\to+\infty$. More precisely, the restriction to the diagonal
$\chi(k^{-1}T_R)(x,x)$ decays at the rate $O(k^{-\infty})$ in the interior and
has an asymptotic expansion on the boundary with leading term of order
$k^{n+1}$ expressed in terms of the Levi form and the pairing of the contact
form with the vector field $R$.
