Abstract: City crimes tend to be clustered spatially and temporally. Knox test is an effective way to detect such interactions, however, this method has been criticized as being subjective because the determination of critical distances is arbitrary. This paper begins with an introduction of the Knox test and some common methods to select the spatial thresholds. Then a new approach is proposed to detect critical distances based on the average nearest neighborhood distance. Burglary, electric vehicle theft and pick pocketing events in Wuhan city are used as experimental data to validate the method. Results show that, compared with four common criteria, i.e., empirical distance, mean distance, Ripley's K function threshold and natural breaks classification, the method we proposed is able to detect spatio-temporal interaction patterns of different events more effectively. The analysis results provide a reference for selecting critical distances for the Knox test.