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A new CdZnTe gamma-ray spectrometer system that employs two layers of modular detector arrays Is being developed under the collaboration between the University of Michigan and the Pacific Northwest National Labaratory (PNNL). Each layer can accommodate up to three by three 3-dimensional position sensitive CdZnTe gamma-ray spectrometers. This array system is based on the newly developed VAS_UM/TAT4 ASIC readout electronics. Each of the nine detector modules consists of a pixellated CdZnTe detector and a VAS_UM/TAT4 ASIC front-end board. Each 1.5times1.5times1.0 cm3 CdZnTe detector employs an array of 11 by 11 pixellated anodes and a planar cathode. The energy depositions and 3-dimensional positions of individual interactions of each incident gamma ray can be obtained from pulse amplitude, location of each pixel anode and the drift time of electrons. Ten detectors were tested individually and half of them achieved resolution of <1.0% FWHM at 662 keV for single-pixel events (~30% of all 662 keV full energy deposition events). Two of them were tested in a simple array to verify that the upgrade to an array system does not sacrifice the performance of individual detectors. Experimental results of individual detectors and a two-detector array system are presented, and possible causes for several worse performing detectors are discussed.