The hard X-ray imager (HXI) and soft gamma-ray detector (SGD) onboard Astro-H observe astronomical objects with high sensitivity in the hard X-ray (5-80 keV) and soft gamma-ray (40-600 keV) energy bands. To achieve this high sensitivity, background rejection is essential, and these detectors are surrounded by large and thick bismuth germinate scintillators as an active shield. We have developed adequate trigger logic for both the HXI and SGD to process signals from main detector and BGO shield simultaneously and then we optimized the trigger delay and width, with consideration of the trigger latch efficiency. The shield detector system performs well, even after it is assembled as the HXI sensor. The energy threshold maintains the same level as that observed during the prototype development phase, and the experimental room background level of the main detector is successfully reduced by our optimized trigger timing.