We perform a chi ^{2} fit at 95% CL to obtain model-dependent bounds to Z-Z' mixing angle theta and Z_2-mass in the framework of SU(3)_C X SU(3)_L X U(1)_X models with beta arbitrary. Using experimental results at the Z-pole and atomic parity violation, we obtain allowed regions according to the value of beta and depending on the assignment of the quark families in mass eigenstates into the three different families in weak eigenstates that cancel anomalies.