The Minnesota Historical Society has a free lookup for births and deaths that occurred in the state.
Births: from 1900-1934, and selected records from pre-1900
Deaths: from cards 1904 to 1907 and death certificates from 1908 to 2001
This site also has a database index to state census records for the years 1865, 1875, 1885, 1895 and 1905. If you have family connections in Minnesota you should explore this site to see what else you can find.