Video-based person re-identification (ReID) has become increasingly important due to its applications in video surveillance applications. By employing events in video-based person ReID, more motion information can be provided between continuous frames to improve recognition accuracy. Previous approaches have assisted by introducing event data into the video person ReID task, but they still cannot avoid the privacy leakage problem caused by RGB images. In order to avoid privacy attacks and to take advantage of the benefits of event data, we consider using only event data. To make full use of the information in the event stream, we propose a Cross-Modality and Temporal Collaboration (CMTC) network for event-based video person ReID. First, we design an event transform network to obtain corresponding auxiliary information from the input of raw events. Additionally, we propose a differential modality collaboration module to balance the roles of events and auxiliaries to achieve complementary effects. Furthermore, we introduce a temporal collaboration module to exploit motion information and appearance cues. Experimental results demonstrate that our method outperforms others in the task of event-based video person ReID.