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.
To my knowledge, Arizona’s Democrats and Republicans are the only parties that are letting state law intimidate them into allowing independents into their primaries. AZ’s Libertarians won a federal suit in 2007 that lets them block independents from their primaries.
Under a state attorney general’s opinion, Nebraska gives independents their choice of primary in congressional elections. This is because independents are able to vote in the “nonpartisan primary” for the state legislature, which, of course, is elected on a nonpartisan basis.
Rep Gerald Neal (D) is also a co-sponser of this legislation. Independents here in Kentucky should, in my opinion, be allowed to partisipate in Primaries.