From Halopedia, the Halo wiki
UNSC Burden of Proof was a starship of unknown class in service with the UNSC Navy during 2552. On August 30th, Dr. Catherine Halsey sent an official protest backed up by Vice Admiral Michael Stanforth regarding Colonel James Ackerson's involvement in a test of artificial intelligence integration into the Mark V MJOLNIR armor in which John-117 was nearly killed. In the report, Halsey suggested that Ackerson may have suffered a mental breakdown and advised that he be taken into custody.
Given its name and the fact that Dr. Halsey sent the vessel a message concerning a judicial matter, the Burden of Proof may have been affiliated with the UNSC Judge Advocate General's Corps.