Real-time scheduling for Mixed-Criticality (MC) systems has received a growing attention as real-time embedded systems accommodate various tasks with different levels of criticality. While many studies have addressed how to guarantee timing requirements for MC systems with uniprocessor and multiprocessors, most of them have focused on supporting preemptive tasks. On the other hand, there have been few studies to address non-preemptive scheduling especially for MC multiprocessor platforms, in which the jobs under execution cannot be preempted by other jobs. In this paper, we develop schedulability tests for non-preemptive scheduling, which is the first attempt for MC multiprocessor systems. To this end, we first generalize an existing NP-EDF (Non-Preemptive Earliest Deadline First) schedulability test developed for single-criticality multiprocessor systems, towards for MC multiprocessor systems. For the generalization, we introduce new timing guarantee techniques for the system transition between two different criticalities, which is one of the key features in MC systems. We next extend the proposed NP-EDF schedulability test towards NP-EDFVD (NP-EDF with Virtual Deadlines) that is specialized for MC systems, and pose a virtual deadline assignment problem. We develop an optimal virtual deadline assignment policy using a control knob of the system-level deadline-reduction parameter and then a suboptimal one for the task-level parameter. Our simulation results demonstrate that the NP-EDFVD schedulability test with the proposed virtual deadline assignment policies finds a number of additional schedulable task sets, which are not schedulable by the NP-EDF schedulability test.