Answer: To some extent it depends what you are shipping, where it originates and where it is going. California, for instance, has very strict rules.
Your state department of agriculture should be able to help you, you might also start with your local county Extension for some direction to the state level.
The US Department of Agriculture and APHIS also regulate plant movement and in some cases soil associated with plants.
Their web site may provide some answers for you as well. For instance, here is their page about permits.
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