We present the results of a search for a very light CP-odd Higgs boson a01 originating from top quark decays t→H±b→W±(*)a01b, and subsequently decaying into τ+τ−. Using a data sample corresponding to an integrated luminosity of 2.7  fb−1 collected by the CDF II detector in pp 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 a01.