Out dated and fixed, New way to obtain zombie is as follows:
"January 30th, 2012
Zombies are now only able to spread the infection through
cannibalism. Cannibalism's cooldown has been lowered from 45
to 20 seconds as well." ~Zodiac News
It works this way, if you are dead (don't have to be killed by a zombie) and a Zombie casts Cannibalism on you, You will have a small chance on obtaining an Infected vial which is the Zombie Essence. The Exact drop rate has been changed but will not be disclosed or given out. There are a couple other safeties in place to prevent the Infected Vial from being spammed non stop.
Further questions can be aimed towards a GP, FP4, or Ketso in game.