Mythbusters decided to test whether an inmate could "kill another inmate across the hall using a crossbow made of newspaper":
"Jamie and Adam built separate crossbows for the myth and fired a few shots each. Testing proved that it is possible to kill someone using a paper crossbow, but it would require a precise shot to a vital spot (like a major blood vessel in the neck), which is difficult with improvised weapons such as a paper crossbow. The crossbows each became useless after a few shots, further showing that the shooter would have only a single shot to hit a vital spot."
Inspired by Mythbusters, YouTube's ChuKoNu1 created his own. Check his out below, and scroll down further to see how it's made.
Mythbusters demonstrates how it's done: