The Libertarian Party has had nominees on the ballot for Governor and/or U.S. Senator in all 50 states. But only in Tennessee have the Libertarian nominees been unable to have their party label on the ballot, except in 2000.
When one examines the best percentage ever for a Libertarian for Governor or U.S. Senator in each state, in only three states is there no instance when a Libertarian for those offices managed to get as much as 1%. They are Tennessee, Maine, and Rhode Island. The main reason there are no such examples in Maine and Rhode Island is that there have been so few Libertarians on the ballot for Governor and U.S. Senate in those two states. Rhode Island is the only state in which the party has never been on the ballot for U.S. Senate.
In Tennessee, minor party nominees suffer because they only have the label “independent” next to their names, and most voters don’t know who the minor party nominees are. Tennessee won’t permit party labels except for qualified parties, and the petition to be a qualified party is so difficult, no group has ever used it since 1968, when George Wallace’s American Party did it. It requires 56,083 signatures.