We report on the results of a search for a Weakly Interacting Massive Particle (WIMP) signal in low-energy data of the Cryogenic Dark Matter Search experiment using a maximum likelihood analysis. A background model is constructed using geant4 to simulate the surface-event background from Pb210 decay-chain events, while using independent calibration data to model the gamma background. Fitting this background model to the data results in no statistically significant WIMP component. In addition, we perform fits using an analytic ad hoc background model proposed by Collar and Fields, who claimed to find a large excess of signal-like events in our data. We confirm the strong preference for a signal hypothesis in their analysis under these assumptions, but excesses are observed in both single- and multiple-scatter events, which implies the signal is not caused by WIMPs, but rather reflects the inadequacy of their background model.