As I understand it*...
As a private party, you can sell any non-NFA gun to anyone you want to, as long as they are at least 18 years old. There is no requirement for them to prove they are eligible to own/possess a firearm. In addition, there is no requirement that you report the sale/transfer to local law enforcement.
For non-dealers, this is really all you need to know...
Subd. 12.Exclusions. Except as otherwise provided in section 609.66, subdivision 1f, this section shall not apply to transfers of antique firearms as curiosities or for their historical significance or value, transfers to or between federally licensed firearms dealers, transfers by order of court, involuntary transfers, transfers at death or the following transfers:
(1) a transfer by a person other than a federally licensed firearms dealer;
In the above quoted instance, "section" refers to the entire statute (624.7132).
*Disclaimer: I am not a legal expert, I do not work in law enforcement, I am not an FFL, nor am I a legislator.
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