Whether different sources of mortality are additive, compensatory, or depensatory is a key question in population biology. A way to test for additivity is to calculate the correlation between cause-specific mortality rates obtained from marked animals. However, existing methods to estimate this correlation raise several methodological issues. One difficulty is the existence of an intrinsic bias in the correlation parameter. Although this bias can be formally expressed, it requires knowledge about natural survival without any competing mortality source, which is difficult to assess in most cases. Another difficulty lies in estimating the true process correlation while properly accounting for sampling variation. Using a Bayesian approach, we developed a state-space model to assess the correlation between two competing sources of mortality. By distinguishing the mortality process from its observation through dead recoveries and live recaptures, we estimated the process correlation. To correct for the intrinsic bias, we incorporated experts' opinions on natural survival. We illustrated our approach using data on a hunted population of wild boars. Mortalities were not additive and natural mortality increased with hunting mortality likely as a consequence of non-controlled mortality by crippling loss. Our method opens perspectives for wildlife management and for the conservation of endangered species.