On October 7, a U.S. District Court in Hawaii held a trial in Democratic Party of Hawaii v Nago, 1:13cv-301. According to this story, Judge J. Michael Seabright has not decided the case yet, but he did indicate that if he concludes that the Hawaii law imposes a severe burden on the Democratic Party, he will strike it down.
The lawsuit was filed by the party to escape the open primary, and to let the party restrict its primary to party members. Presumably if the party wins the case, the state will begin asking voters to choose a party on voter registration forms. Currently, Hawaii voter registration forms do not ask about party membership. When the Idaho Republican Party won a similar lawsuit, the legislature changed the voter registration forms to include a party membership question.