The proposition that life can spread from one planetary system to another (interstellar panspermia) has a long history, but this hypothesis is difficult to test through observations. We develop a mathematical model that takes parameters such as the microbial survival lifetime, the stellar velocity dispersion, and the dispersion of ejecta into account in order to assess the prospects for detecting interstellar panspermia. We show that the correlations between pairs of life-bearing planetary systems (embodied in the pair-distribution function from statistics) may serve as an effective diagnostic of interstellar panspermia, provided that the velocity dispersion of ejecta is greater than the stellar dispersion. We provide heuristic estimates of the model parameters for various astrophysical environments and conclude that open clusters and globular clusters appear to represent the best targets for assessing the viability of interstellar panspermia.