The most general Lorentz-invariant spin-correlation functions for ${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\rho}}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\nu}, ${\mathit{a}}_{1}^{\mathrm{\ensuremath{-}}}$\ensuremath{\nu}, ${\mathit{K}}^{\mathrm{*}\mathrm{\ensuremath{-}}}$\ensuremath{\nu}, ${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\nu}, ${\mathit{K}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\nu} are expressed in terms of eight semileptonic parameters. The parameters are physically defined in terms of \ensuremath{\tau}-decay partial-width intensities for polarized final states. The parameters are also expressed in terms of a ``(V-A) + additional chiral coupling'' structure in the ${\mathit{J}}_{\mathrm{lepton}}^{\mathrm{charged}}$ current, so as to bound effective-mass scales \ensuremath{\Lambda} for ``new physics'' such as arising from lepton compositeness, leptonic CP violation, leptonic T violation, \ensuremath{\tau} weak magnetism, weak electricity, and/or second-class currents. The two tests for leptonic CP violation in \ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\nu} decay are generalized to \ensuremath{\tau}\ensuremath{\rightarrow}${\mathit{a}}_{1}$\ensuremath{\nu} decay and to two additional tests if there are ${\ensuremath{\nu}}_{\mathit{R}}$ and \ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{L}}$ couplings. For ${10}^{7}$(${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}}$,${\mathrm{\ensuremath{\tau}}}^{+}$) pairs at 10 GeV, from the {${\mathrm{\ensuremath{\rho}}}^{\mathrm{\ensuremath{-}}}$,${\mathrm{\ensuremath{\rho}}}^{+}$} mode and using the four-variable distribution ${\mathit{I}}_{4}$, the ideal statistical percentage errors are, for \ensuremath{\xi}, 0.6%, for \ensuremath{\zeta}, 0.7%, for \ensuremath{\sigma}, 1.3%, and for \ensuremath{\omega}, 0.6%. CP tests are typically \ensuremath{\surd}2 worse. Parameters sensitive to leptonic T violation are \ensuremath{\omega}, and the following from the {${\mathit{a}}_{1}^{\mathrm{\ensuremath{-}}}$,${\mathit{a}}_{1}^{+}$} mode: using ${\mathit{I}}_{5}^{\mathrm{\ensuremath{-}}}$ the errors are, for \ensuremath{\eta}, 0.6%; using ${\mathit{I}}_{7}$, for \ensuremath{\eta}\ensuremath{'}, 0.013; and using ${\mathit{I}}_{7}^{\mathrm{\ensuremath{-}}}$, for \ensuremath{\omega}\ensuremath{'}, 0.002. In the future, by stage-two spin-correlation techniques, polarized-partial-width measurements should be useful in studying top quark, ${\mathit{W}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\mathit{Z}}^{0}$, and Higgs boson decays. \textcopyright{} 1996 The American Physical Society.