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We report orientational imaging of the polarization distribution in nanostructured ferroelectric copolymer of polyvinylidene fluoride-trifluoroethylene (PVDF-TrFE) and collagen fibrils using vertical and lateral modes of piezoresponse force microscopy (PFM). In PVDF-TrFE, detection of azimuthal variations in the lateral PFM signal is attributed to the alignment of the molecular chains along different directions. Local switching in PVDF-TrFE is shown to proceed via 120° or 180° rotation of dipoles around the molecular chain, depending upon the strength of the applied electric field. Analysis of the vertical and lateral PFM signals in collagen reveals polar anisotropy of the electromechanical properties along the axes of the fibrils. The surface plots of the piezoelectric response are constructed for both materials based on their piezoelectric tensors and are shown to be consistent with the observed vertical and lateral PFM maps.