Kentucky has registration by party, and does not allow independents to vote in party primaries. Although (under a U.S. Supreme Court decision) any party with a primary is free to override state law and let independents vote in its primary, neither the Democratic nor Republican Party currently allows independents to vote in its primaries.
Kentucky Representative Jimmy Higdon (R-Lebanon) has introduced HB 17, which says that independent voters may vote in any party primary. The bill does not acknowledge any role for political parties to make their own decision about that.