We are investigating the feasibility of a high resolution positron emission tomography (PET) insert device based on the CdZnTe detector with 350 µm anode pixel pitch to be integrated into a conventional animal PET scanner to improve its image resolution. In this paper, we have used a simplified version of the multi pixel CdZnTe planar detector, 5 mm thick with 9 anode pixels only. This simplified 9 anode pixel structure makes it possible to carry out experiments without a complete application-specific integrated circuits readout system that is still under development. Special attention was paid to the double pixel (or charge sharing) detections. The following characteristics were obtained in experiment: energy resolution full-width-at-half-maximum (FWHM) is 7% for single pixel and 9% for double pixel photoelectric detections of 511 keV gammas; timing resolution (FWHM) from the anode signals is 30 ns for single pixel and 35 ns for double pixel detections (for photoelectric interactions only the corresponding values are 20 and 25 ns); position resolution is 350 µm in x,y-plane and ~0.4 mm in depth-of-interaction. The experimental measurements were accompanied by Monte Carlo (MC) simulations to find a limitation imposed by spatial charge distribution. Results from MC simulations suggest the limitation of the intrinsic spatial resolution of the CdZnTe detector for 511 keV photoelectric interactions is 170 µm. The interpixel interpolation cannot recover the resolution beyond the limit mentioned above for photoelectric interactions. However, it is possible to achieve higher spatial resolution using interpolation for Compton scattered events. Energy and timing resolution of the proposed 350 µm anode pixel pitch detector is no better than 0.6% FWHM at 511 keV, and 2 ns FWHM, respectively. These MC results should be used as a guide to understand the performance limits of the pixelated CdZnTe detector due to the underlying detection processes, with the understanding of the inherent limitations of MC methods.