Conjunction analysis is the study of possible collisions between objects in space. This analysis is typically aimed at reducing the number of collisions between man-made objects and debris currently orbiting the Earth. A standard approach requires the computation of all possible interactions in orbit. A new method is proposed utilizing a kd-tree along with the Hellinger distance to determine the probability of collision between space debris. It is assumed that all debris is of negligible size, with Gaussian errors in position. It is found that kd-tree based methods significantly reduce computational cost while obtaining comparable results.