The "paper" you are putting together refers to this evidence-gathering scene. Here is the context of the episode:
: They track the gun to a woman named "Miss Birdy," who informs them she threw away the materials the gun was wrapped in. [S2E4] Chicken, Dynamite, Chainsaw
Chicken, Dynamite, Chainsaw - Chicago P.D. (Season 2, Episode 4) The "paper" you are putting together refers to
: The "Chicken, Dynamite, Chainsaw" game decides who has to go into the dumpster to retrieve the discarded items. (Season 2, Episode 4) : The "Chicken, Dynamite,
They use the game to determine who has to perform the unpleasant task of for evidence—specifically the paper and rags that a triple homicide weapon was wrapped in.
: Burgess and Roman are assigned to a gun buyback program but discover a weapon linked to a triple homicide.
In Season 2, Episode 4, titled " Chicken, Dynamite, Chainsaw ," the phrase refers to a specific version of Rock, Paper, Scissors played by officers Burgess and Roman.