The Judicium was a Peacekeeper organization. It apparently carried out legal functions within the Peacekeeper military structure.
When Lieutenant Macton Tal informed Captain W'Lash of the birth of Ka Jothee, W'Lash was able to get the Judicium to convene to discuss the matter. While the union between a Sebacean and Luxan was displeasing, the birth of a hybrid was enough to get them interested in the matter, as up until the birth itself, its members had been unconvinced such a child could ever be born. The Judicium called for immediate hearings on the subject, and the physician who supervised the birth was brought in for questioning. However, because the offspring's parents, Ka D'Argo and Lo'Laan Tal had left Havenik by this point, and settled on a planet on the outskirts of the Uncharted Territories, the Judicium dropped the matter, as the family could not be traced. ("Brotherly Hate")