The CoGeNT Collaboration has recently published results from a fifteen month data set which indicate an annual modulation in the event rate similar to what is expected from weakly interacting massive particle interactions. It has been suggested that the CoGeNT modulation may actually be caused by other annually modulating phenomena, specifically the flux of atmospheric muons underground or the radon level in the laboratory. We have compared the phase of the CoGeNT data modulation to that of the concurrent atmospheric muon and radon data collected by the MINOS experiment which occupies an adjacent experimental hall in the Soudan Underground Laboratory. The results presented are obtained by performing a shape-free χ2 data-to-data comparison and from a simultaneous fit of the MINOS and CoGeNT data to phase-shifted sinusoidal functions. Both tests indicate that the phase of the CoGeNT modulation is inconsistent with the phases of the MINOS muon and radon modulations at the 3.0σ level.