Fully polarimetric scanning and vertically pointing Doppler spectral data from the state-of-the-art Stony Brook University Ka-band Scanning Polarimetric Radar (KASPR) are analyzed for a long-duration case of ice pellets over central Long Island in New York from 12 February 2019. Throughout the period of ice pellets, a classic refreezing signature was present, consisting of a secondary enhancement of differential reflectivity ZDR beneath the melting layer within a region of decreasing reflectivity factor at horizontal polarization ZH and reduced copolar correlation coefficient ρhv. The KASPR radar data allow for evaluation of previously proposed hypotheses to explain the refreezing signature. It is found that, upon entering a layer of locally generated columnar ice crystals and undergoing contact nucleation, smaller raindrops preferentially refreeze into ice pellets prior to the complete freezing of larger drops. Refreezing particles exhibit deformations in shape during freezing, leading to reduced ρhv, reduced co-to-cross-polar correlation coefficient ρxh, and enhanced linear depolarization ratio, but these shape changes do not explain the ZDR signature. The presence of columnar ice crystals, though apparently crucial for instigating the refreezing process, does not contribute enough backscattered power to affect the ZDR signature, either.