  We examine the possibility of using rare, 3-body decays of a new neutral
gauge boson, \ztwo, to probe its gauge couplings at hadron colliders.
Specifically, we study the decays $\ztwo\to W\ell\nu$ and $\ztwo\to
Z\nu\bar\nu$ and find that much knowledge of the \ztwo\ properties can be
obtained from these processes. In particular, these decay modes can yield
valuable information on the amount of $Z_1-Z_2$ mixing, on the generation
dependence of the \ztwo\ couplings, on the properties of the new generator
associated with the \ztwo, as well as being used to distinguish between
possible extended models. The analogous 3-body decays into a new, heavy charged
gauge boson, $\ztwo\to W_2^\pm\ell^\mp\nu$, are also investigated in models
where this can occur.
