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What is that, the NFA?
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It is indeed. 26 USC 5841, to be precise. It applies to machine guns, destructive devices and AOWs.
Who has the right to ask to see this?
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The person to whom proof of registration must be shown is the the Secretary of the Treasury and his agents. In other words, BATF. It would not be smart to fail to show proof of registration to any other LEO who might request it, since it is illegal to possess these things without registering them.
Can you be detained prior to making this available?
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Can you be detained for driving without a license or failing to provide proof of insurance? You bet.
What is the crime associated with not making this available?
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As for the penalty for failing to make the information available to the Secretary on request:
"Any person who violates or fails to comply with any provisions of this chapter shall, upon conviction, be fined not more than $10,000, or be imprisoned not more than ten years, or both."
26 USC 5871. But that's not all:
"Any firearm involved in any violation of the provisions of this chapter shall be subject to seizure and forfeiture...."
26 USC 5872.