  In the framework of general 3-3-1 models, we perform a global $\chi ^2$ fit
at $95\%$ C.L. to the updated Z pole observables, including new data from
atomic parity violation. We found scenarios where specific realizations of
3-3-1 models are largely excluded above the current limit on the extra neutral
gauge boson ($Z'$) research at LHC. We derive a relation between the $Z-Z'$
mixing angle and the parameter $\tan(\beta)$ of the effective Two-Higgs-Doublet
Model contained into the 3-3-1 spectrum. We show that particular versions of
3-3-1 models containing particles with exotic electric charges are disfavored
by the electroweak precision observables in an ample region of the parameter
space.
