  This paper reports a measurement of the cross section for the pair production
of top quarks in ppbar collisions at sqrt(s) = 1.96 TeV at the Fermilab
Tevatron. The data was collected from the CDF II detector in a set of runs with
a total integrated luminosity of 1.1 fb^{-1}. The cross section is measured in
the dilepton channel, the subset of ttbar events in which both top quarks decay
through t -> Wb -> l nu b where l = e, mu, or tau. The lepton pair is
reconstructed as one identified electron or muon and one isolated track. The
use of an isolated track to identify the second lepton increases the ttbar
acceptance, particularly for the case in which one W decays as W -> tau nu. The
purity of the sample may be further improved at the cost of a reduction in the
number of signal events, by requiring an identified b-jet. We present the
results of measurements performed with and without the request of an identified
b-jet. The former is the first published CDF result for which a b-jet
requirement is added to the dilepton selection. In the CDF data there are 129
pretag lepton + track candidate events, of which 69 are tagged. With the
tagging information, the sample is divided into tagged and untagged
sub-samples, and a combined cross section is calculated by maximizing a
likelihood. The result is sigma_{ttbar} = 9.6 +/- 1.2 (stat.) -0.5 +0.6 (sys.)
+/- 0.6 (lum.) pb, assuming a branching ratio of BR(W -> ell nu) = 10.8% and a
top mass of m_t = 175 GeV/c^2.
