  We propose a generalization of the coherent anomaly method to extract the
critical exponents of a phase transition occurring in the steady-state of an
open quantum many-body system. The method, originally developed by Suzuki [J.
Phys. Soc. Jpn. {\bf 55}, 4205 (1986)] for equilibrium systems, is based on the
scaling properties of the singularity in the response functions determined
through cluster mean-field calculations. We apply this method to the
dissipative transverse-field Ising model and the dissipative XYZ model in two
dimensions obtaining convergent results already with small clusters.
