We present a detailed study of the heavy flavor content in the W
+ jet data sample collected with the CDF detector during the 1992-1995
collider run at Fermilab.  Rates of heavy flavor jets, identified via the
observation of secondary vertices or semileptonic decays of b and c quarks,
are in good agreement with a standard model simulation including production
of the top quark.  An exception is the number of events in which a single
jet has both a secondary vertex and a semileptonic decay tag.  In the W +
2,3 jet data, we expect 4.4 +/- 0.6 and we find 13 such events.  The
kinematic properties of this small sample of events are statistically
difficult to reconcile with the simulation of standard model processes.