We present new, high resolution (2\AA \ FWHM) spectroscopic data for M32. The data covers the spectral range from 3500\AA-4500\AA. The system of spectral indices developed by Rose (1994, A.J. , 107 , 206) to study variations in stellar populations between galaxies is used to look for line strength gradients in M32. We find no significant gradients out to 30," which was the useful extent of our data. A comparison is made with the recent study of Hardy et al. (1994, A.J. , 107 , 195). Using the Lick indices (Mg$_{2}$, H$\beta$, Fe), centered in the red (5000\AA), they detected gradients in the outer regions of the galaxy, but found the line strengths were constant with radius out to 30." A comparison is made with studies of broadband color gradients, as well. Implications for radial variations in the stellar populations are discussed.