In the forensics context, we are often tasked with deciding whether two items have a common source. An empirically derived approach uses a classification rule based on differences between measurements obtained from pairs of objects known to have originated from the same or from a different source.  These differences are combined into a similarity score using a learning method such as a random forest. While this approach has been shown to perform well in practice, there is loss of information in going from multiple measurements to a single score, and results are difficult o explain to lay persons.  Here, we propose an explicit decision rule that is obtained by minimizing the weighted sum of the false positive and false negative error probabilities.  We show that the proposed rule maximizes true positive rate while controlling for the false positive rate at a desired level.  We evaluate the performance of the rule via simulation and illustrate its implementation with a real dataset that includes measurements of 17 elemental concentrations on glass fragments.