We have analyzed archival ROSATPSPC data for M32 in order to study the X-ray emission from this nearest elliptical galaxy. We fitted spectra from three long exposures with Raymond-Smith, thermal bremsstrahlung, and power-law models. All models give excellent fits. The thermal fits have kT approximate to 4 keV, the Raymond-Smith iron abundance is 0.4(-0.3)(+0.7) solar, the power-law fit has alpha = 1.6 +/- 0.1, and all fits have N-H consistent with the Galactic column. The source is centered on M32 to an accuracy of 9 '', and unresolved at 27 '' FWHM (similar to 90 pc). M32 is X-ray variable by a factor of 3-5 on timescales of a decade down to minutes, with evidence for a possible period of similar to 1.3 days. There are two plausible interpretations for these results: (1) emission due to low-mass X-ray binaries; (2) emission due to accretion onto a massive central black hole. Both of these possibilities are supported by arguments based on previous studies of M32 and other old stellar systems; the ROSAT PSPC data do not allow us to unambiguously choose between them. Observations with the ROSAT HRI and with ASCA are required to determine which of these two very different physical models is correct.