  We present the results of a search for a very light CP-odd Higgs boson
$a_1^0$ originating from top quark decays t -> H^+ b -> W^+ a_1^0 b, and
subsequently decaying into tau-tau. Using a data sample corresponding to an
integrated luminosity of 2.7 inv fb collected by the CDF II detector in
p-anti-p collisions at 1.96 TeV, we perform a search for events containing a
lepton, three or more jets, and an additional isolated track with transverse
momentum in the range 3 to 20 GeV/c. Observed events are consistent with
background sources, and 95% C.L. limits are set on the branching ratio of t ->
H^+ b for various masses of H^+ and a_1^0.
