The Daily Record of York, Pennsylvania, has this article explaining the legal status of the Pennsylvania Libertarian Party. Because, in 2012, the party met the vote test for “political party” status, it has a few advantages, as the story explains. In particular, for an upcoming special legislative election, the Libertarian Party can choose a nominee without any need for a petition.
Until 1986, if a party in Pennsylvania met the 2% vote test and became a “party”, that meant it was automatically on the ballot for all partisan office. But in 1986 the legislature passed a law that said parties are not automatically on the ballot in regularly-scheduled elections unless they have registration membership of at least 15% of the state total (which would be over 1,000,000 registered voters). If that law were in effect in Massachusetts, District of Columbia, Utah, or Idaho, one or the other of the two major parties would not be on the ballot.
The 1986 law change did not change procedures for special elections.