  $Z$ production at an $e^+e^-$ collider, associated with production of other
particles, can be an accurate source of information of details of electroweak
interactions, including possible interactions beyond the standard model. We
discuss from a general physical point of view the properties of the density
matrix as well as lepton angular asymmetries. While most considerations will be
applicable to processes of $Z$ production associated with any other particle or
particles, for some discussions, we specialize to a $HZ$ final state. While
many of the results can be found in earlier literature, especially for the
process $e^+e^- \to HZ$, we give details of the reasoning, which are not always
found. We discuss the properties of the spin density matrix under C, P and T
transformations, and combinations thereof, as also the predictions of these for
the corresponding leptonic asymmetries. The specific transformations P, CP, T
and CPT are of special importance and we discuss the consequences of these
symmetries or their absence for the leptonic asymmetries. A specific issue
which has been given attention to is the role of beam polarization, and how one
can infer on general grounds which asymmetries get enhanced by the use of beam
polarization. Similarly, we also discuss which asymmetries would be sensitive
to the measurement of tau polarization in $Z$ decay in to $\tau^+\tau^-$.
