"On Tuesday you will start the day with a Clipboard in your hands. Walk up to people and press fire to ask them to sign your petition. Be persistent! Some people may not sign it at first but may change their minds if you ask again. And again. Other people (even cops!) may attack you if you bother them too much!
The Clipboard is always in your hands until you get enough names to complete the errand, at which point it is automatically put away. You cannot drop the clipboard and you will not lose it if you get sent to jail. When you press E to put away your weapons, you will end up holding the clipboard." — The petition's description in the manual
The Petition is an item and "weapon" featured in Postal 2. Primary fire asks people if they want to sign the petition. The goal of the petition is to "Make Whiney Congressmen Play Violent Video Games." At the start of Tuesday, the Postal Dude is given the item and is tasked with getting 8 more signatures from civilians. If a civilian refuses, the Postal Dude can try 2 more times. The 3rd time will be a threatening retort/death threat, and can result in the citizen running away in terror to call the Police, or rarely retaliate themselves. RWS employees will usually agree on the first or second try. Cops will never sign the petition, and try to arrest or attack you after the 3rd try. Terrorists however will only sign on the third try. After getting 8 signatures, the Postal Dude will put the Petition away, making it is unavailable for the rest of the game. The petition cannot be dropped, but will be removed if the Dude is arrested.
In Postal 2 Complete if the player is on the higher difficulties, the petition mission is automatically skipped since every armed NPC will attack the Postal Dude instantly, and the Police Uniform does not exist in the police station.