Kentucky requires candidates for state office who are running outside the qualified parties to file a declaration of candidacy by April 1. This year, only one minor party candidate, and three independent candidates, filed for the state legislature (which is the only state office up in 2016). The declaration of candidacy filing requirement does not apply to federal office. See this story. The only minor party candidate is a Libertarian.
Last time Kentucky held legislative elections, in 2014, there were no minor party candidates, and only two independent candidates.
Petitions for these candidates are not due until August, and require 100 signatures.