Currently, qualified parties in New Hampshire decide for themselves whether to let independent voters vote in their primaries. On February 22, the House Election Law Committee defeated HB 642. It would have mandated that all New Hampshire primaries be closed, meaning only registered members of that party could vote in that party’s primary. See the bill text. The bill lost unanimously, 20-0. The author is Representative Norman Silber (R-Gilford).
Your link for “see this story” links to the text of the bill.
PS
a Senate Bill (SB114) “prohibiting a candidate from receiving the nomination of more than one party” received a favorable vote in Committee, and has a floor vote on March 9.
On that point, NH does it right. Let the parties decide.
IMO, parties should also decide themselves whether or not to cross endorse.