I'm not a teacher, but after reading this several times, I took it it to be using "trajectory" to mean simply, "path" or "course". So the body, once dead, followed a trajectory of its own, being passed around various people (the "responding officers"?), each of whom, added their own paperwork to the collection of documentation accompanying the body. At the end of the "trajectory", the body was "paper-strewn".
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