We present a polarimetric investigation of the protoplanetary nebula Frosty Leo performed with the Submillimeter Array. We were able to detect, in the low continuum level (peak at 14.4 mJy beam$^{-1}$), a marginal polarization at $sim2.6sigma$. The molecular line investigation based on the CO $J=3rightarrow2$ emission shows a peak emission of 68.1 Jy beam$^{-1}$ km s$^{-1}$ and the polarization detection in this CO line is also marginal, with a peak at $sim3.8sigma$. In both cases, it was therefore not possible to use the electric vector maps (B-field) to accurately trace the magnetic field (B-field) within the PPN. The spatio-kinematic modelling realised with the different velocity channel maps indicates three main structures: a distorted torus accompanied by a bipolar outflow or jet aligned with its axis and a flattened spherical cap. The comparison of the CO polarization segments with our model suggests that the polarized emission probably arises in the first two components.