I'm a gun dealer (though not in MN), and as such I have to follow all state as well as federal laws for firearm transfers. For example, I could legally transfer a bolt-action rifle or pump shotgun to you, but not the semi-automatic rifles defined as "assault weapons".
In addition to a rather thick book provided to me by the ATF, one of the best resources I've found when looking up a state's laws is the NRA-ILA web site. For your situation: http://www.nraila.org/statelawpdfs/MNSL.pdf.
For MN I didn't find out how to appeal the denial of a handgun purchase permit. There is a process to appeal the denial of a concealed carry permit. So, if I were you, I'd apply for a concealed carry permit. If one is issued, all well and good since it also can be used to purchase a handgun. If not, you simply file a complaint in your local District court, which is much cheaper and faster than going to Federal court.

