  We report a study of multi-muon events produced at the Fermilab Tevatron
collider and recorded by the CDF II detector. In a data set acquired with a
dedicated dimuon trigger and corresponding to an integrated luminosity of 2100
pb$^{-1}$, we isolate a significant sample of events in which at least one of
the identified muons has large impact parameter and is produced outside the
beam pipe of radius 1.5 cm. We are unable to fully account for the number and
properties of the events through standard model processes in conjunction with
our current understanding of the CDF II detector, trigger and event
reconstruction. Several topological and kinematic properties of these events
are also presented. In contrast, the production cross section and kinematics of
events in which both muon candidates are produced inside the beam pipe are
successfully modeled by known QCD processes which include heavy flavor
production. The presence of these anomalous multi-muon events offers a
plausible resolution to long-standing inconsistencies related to $b\bar{b}$
production and decay.
