The Mu2e experiment will search for a neutrinoless
muon-to-electron conversion process with almost four orders of
magnitude of sensitivity improvement relative to the current best
limit. One important background is caused by cosmic-ray muons and
their secondaries faking the conversion electron signature. In order
to reach the designed sensitivity, Mu2e needs to identify cosmic-ray
muons with an efficiency of $>$99.9\%. The Cosmic Ray Veto (CRV)
detector consists of four layers of plastic scintillator which
surrounds the Mu2e detector, with an area of approximately 300
square meters. The CRV must operate in the presence of large neutron
and gamma fluxes produced from beam interactions. This radiation can
damage the detector components and generate significant background
rates in the CRV. We estimate the background rates and the total
dead-time produced by these backgrounds using a simulation which
includes a sophisticated model of the Mu2e apparatus and the CRV
response.