If the Supreme Court states that a law is constitutional, can the same kind of law be written by other states? Why or why not?

No, the others states can not have written the same law because it is a constitutional law which means that the law is already applied to all the states.

I assume this postulates a state statute. A decision upholding the constitutionality of a federal statute might or might not bode well for an equivalent state statute. Some federal laws are within the exclusive province of the federal government, so states may not legislate about the same subject under any circumstances, such as most matters of foreign relations and national defense. There are also categories of law that Congress may choose to make exclusively federal. The Copyright Act of 1976 did that for copyright law, which previously allowed scope for complementary state law.

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