  We present a detailed examination of the heavy flavor content of the $W $ +
jet data sample collected with the CDF detector during the 1992-1995 collider
run at the Fermilab Tevatron. Jets containing heavy flavor quarks are selected
via the identification of secondary vertices or semileptonic decays of $b$ and
$c$ quarks. There is generally good agreement between the rates of secondary
vertices and soft leptons in the data and in the standard model simulation
including single and pair production of top quarks. An exception is the number
of events in which a single jet has both a soft lepton and a secondary vertex
tag. In $W +$ 2,3 jet data, we find 13 such events where we expected 4.4 $\pm$
0.6 events. The kinematic properties of this small sample of events are
statistically difficult to reconcile with the simulation of standard model
processes.
