  Given a CR manifold with non-degenerate Levi form, we show that the operators
of the functional calculus for Toeplitz operators are complex Fourier integral
operators of Szeg\H{o} type. As an application, we establish semi-classical
spectral dimensions for Toeplitz operators. We then consider a CR manifold with
a compact Lie group action $G$ and we establish quantization commutes with
reduction for Toeplitz operators. Moreover, we also compute semi-classical
spectral dimensions for $G$-invariant Toeplitz operators.
