  We study theoretically the squeezing spectrum and second-order correlation
function of the output light for an optomechanical system in which a mechanical
oscillator modulates the cavity linewidth (dissipative coupling). We find
strong squeezing coinciding with the normal-mode frequencies of the linearized
system. In contrast to dispersive coupling, squeezing is possible in the
resolved-sideband limit simultaneously with sideband cooling. The second-order
correlation function shows damped oscillations, whose properties are given by
the mechanical-like, the optical-like normal mode, or both, and can be below
shot-noise level at finite times, $g^{(2)} (\tau) < 1$.
