High-resolution piezoresponse force microscopy (PFM) was used to measure the out-of-plane (effective longtitudinal) and in-plane (effective shear) piezoresponse of zinc oxide films and microrods. Thin films were deposited by pulsed laser deposition (PLD) and micro rods formed from solution. Measurements of three components of piezoresponse, one out-of-plane (OPP) and two in-plane (IPP) signals, allowed the construction of 3D piezoelectric maps reflecting the polycrystalline nature of the films. Both the IPP and OPP piezoresponse signal distributions are analyzed based on the particular texture of the films. It was observed that the central part of microrods contains polarization inversion with head-to-head ferroelectric-like domains. The as-grown domain boundaries were always parallel to the (0001) basal plane. Analysis of the PFM piezoresponse images was done based on the hexagonal structure of ZnO and topographic features along the hexagonal axis.