We present new Hubble Space Telescope Wide-Field Camera 3/infrared medium-band photometry of the compact elliptical galaxy M32, chemically resolving its thermally pulsating asymptotic giant branch stars. We find 2829 M-type stars and 57 C stars. The carbon stars are likely contaminants from M31. If carbon stars are present in M32 they are so in very low numbers. The uncorrected C/M ratio is 0.020+/-0.003; this drops to less than 0.007 after taking into account contamination from M31. As the mean metallicity of M32 is just below solar, this low ratio of C to M stars is unlikely due to a metallicity ceiling for the formation of carbon stars. Instead, the age of the asymptotic giant branch (AGB) population is likely to be the primary factor. The ratio of AGB to red giant branch stars in M32 is similar to that of the inner disc of M31 which contain stars that formed 1.5-4Gyr ago. If the M32 population is at the older end of this age then its lack of C-stars may be consistent with a narrow mass range for carbon star formation predicted by some stellar evolution models. Applying our chemical classifications to the dusty variable stars identified with Spitzer, we find that the x-AGB candidates identified with Spitzer are predominately M-type stars. This substantially increases the lower limit to the cumulative dust-production rate in M32 to >1.20x10^-5^M_{sun}_/yr.