Using experimental results at the Z-pole and atomic parity violation, we perform a chi-squared fit at 95% CL to obtain family-dependent bounds to Z_2 mass and Z-Z' mixing angle in the framework of SU(3)_C X SU(3)_L X U(1)_X models. The allowed regions depend on the assignment of the quark families in mass eigenstates into the three different families in weak eigenstates that cancel anomalies