  We present an analysis of top-antitop quark production and decay into a tau
lepton, tau neutrino, and bottom quark using data from $9 {\rm fb}^{-1}$ of
integrated luminosity at the Collider Detector at Fermilab.
  Dilepton events, where one lepton is an energetic electron or muon and the
other a hadronically-decaying tau lepton, originating from proton-antiproton
collisions at $\sqrt{s} = 1.96 TeV$ are used. A top-antitop quark production
cross section of $8.1 \pm 2.1 {\rm pb}$ is measured, assuming standard-model
top-quark decays. By separately identifying for the first time the single-tau
and the ditau components, we measure the branching fraction of the top quark
into tau lepton, tau neutrino, and bottom quark to be $(9.6 \pm 2.8) %$. The
branching fraction of top-quark decays into a charged Higgs boson and a bottom
quark, which would imply violation of lepton universality, is limited to be
less than $5.9%$ at $95%$ confidence level.
