Various active and passive orbital measurements have provided evidence for surficial water ice within some lunar permanently shadowed regions (PSRs), especially from near-infrared observations by the M³ instrument. However, radar identification of lunar ice has so far remained ambiguous. Here, we examine the radar-inferred dielectric properties of lunar PSRs and illuminated craters to investigate the potential for ice. We show that the dielectric permittivity of proposed surficial ice-bearing PSRs is lower and has a different distribution than illuminated crater floors of the same diameter range. This difference is confirmed via polarimetric analysis. However, we find that regions with fewer or greater numbers of M³ detections do not have meaningfully different dielectric properties. The lack of correlation with M³ detections suggests the differences in radar properties are likely due to a smoother surface at the wavelength scale, perhaps as a consequence of the presence of deeper ice, as suggested by prior studies.