Many people wish to poison squirrels because they view them as "vermin" that harm crops or spread disease. Other people may be curious as to how squirrels can eat so many foods that are poisonous to human beings, such as acorns and poisonous mushrooms.
Geography
It is actually illegal to knowingly poison tree squirrels in most jurisdictions, regardless of their vermin qualities. Some jurisdictions, most notably in California, allow the poisoning of ground squirrels, though a permit is required.
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Types
Squirrels have a short digestive tract that allows them to handle many foods that humans cannot. Because the foods are not in the system long enough to make a difference, trace amounts of poison found in acorns, mushrooms and other problematic natural foods do not bother squirrels.
Most preferred forms of legal poison for squirrels are anti-coagulation poisons. These interfere with blood-clotting abilities of squirrels, leading to their death.
Prevention/Solution
If you feed "the birds," stray cats or any other animals outside, you are inviting a squirrel problem into your yard. Stop feeding any animals outside, and squirrels will have to forage elsewhere.
Considerations
Anti-coagulation poisons need to be fed to ground squirrels on a daily basis for at least five consecutive days in order to be effective. If you have pets or children, these poisons should be in appropriately safe bait-containers.
Warning
Any over-the-counter poison that you purchase to poison squirrels is poisonous to humans and other pets as well.