The phenomenology of an additional (Formula presented) neutral gauge boson (Formula presented) coupled to the third family of fermions is discussed. One might expect such a particle to contribute to processes where taus, (Formula presented) and (Formula presented) quarks are produced. Precision data from CERN LEP1 put severe constraints on the mixing and heavy-boson mass. We find that the effects of such a particle could not be observed at hadronic colliders, be it at the Fermilab Tevatron or the CERN LHC, because of the QCD background. At LEP2 and future (Formula presented) linear colliders, one could instead hope to observe such effects, in particular, for (Formula presented) final states.