Both Kentucky and Tennessee are in the Sixth Circuit. As already noted, on July 2, 2015, the Sixth Circuit struck down Tennessee’s law on how a party remains on the ballot. The Tennessee law let an old party that met the 5% vote test remain on for four years. For example, if it met the vote test in 2010, then it would remain on automatically for both 2012 and 2014. No matter how poorly it did in 2012, it would be on in 2014.
That decision was Green Party of Tennessee v Hargett, 14-5435.
The decision could plausibly be applied to Kentucky. In Kentucky, when a party polls 2% for President, it is then safely on the ballot for four years. For example, John Anderson polled over 2% for President in 1980, under the label “Anderson Coalition.” The Anderson Coalition Party was then safely on the ballot in Kentucky for all elections in 1981 through 1984. The party was on the ballot for President again in November 1984, and since no petition was needed, Anderson appeared on the ballot in Kentucky in 1984 even though he wasn’t running in any other state. It didn’t matter that the Anderson Coalition Party (which had been allowed to re-name itself the National Unity Party) hadn’t even run anyone for any office during 1981, 1982, or 1983.
By contrast, the Libertarian Party got on the ballot for U.S. Senate in Kentucky, and polled 3.08%. The party spent a considerable amount of money on its 2014 petition for U.S. Senate. Once the 2014 election was over, the party was dumped off the ballot and not allowed to participate in 2015 (when Governor is up) or 2016, unless it did an entirely new statewide petition. The petition requirement is 5,000 signatures. It seems plausible that the Kentucky Libertarian Party can rely on the Sixth Circuit Tennessee decision to argue that it should be on the ballot automatically in 2015 and 2016, if not 2018 as well.
The other two states in the Sixth Circuit are Michigan and Ohio. Michigan requires all parties, new and old, to meet the vote test every two years, so there is no discrimination. Similarly, Ohio now allows all parties that qualify (whether by petition or by meeting the 3% vote test) to then be on for four more years. Because the Green Party met the Ohio vote test in 2014, it is on for both 2016 and 2018 (for 2014 only, the Ohio vote test was 2%, but in future elections it is 3%).