In this paper, we study a novel contact tracing query (CTQ) that finds users who have been in $direct$ $contact$ with the query user or $in$ $contact$ $with$ $the$ $already$ $contacted$ $users$ in subsequent timestamps from a large spatio-temporal database. The CTQ is of paramount importance in the era of new COVID-19 pandemic world for finding possible list of potential COVID-19 exposed patients. A straightforward way to answer the CTQ is using traditional spatio-temporal indexes. However, these indexes cannot serve the purpose as each user covers a large area within the time-span of potential disease spreading and thus they can hardly use efficient pruning techniques. We propose a multi-level index, namely QR-tree, that consider both space coverage and the co-visiting patterns to group users so that users who are likely to meet the query user are grouped together. More specifically, we use a quadtree to partition user movement traces w.r.t. space and time, and then exploit these space-time mapping of user traces to group users using an R-tree. The QR-tree facilitates efficient pruning and enables accessing only potential sets of user who can be the candidate answers for the CTQ. Experiments with real datasets show the effectiveness of our approach.