Current New Hampshire law permits write-ins in primaries. The law also says that any write-in candidate in a primary who gets the most votes for a particular office, and who gets at least 10 write-ins, is nominated. HB 1204 would raise that to a minimum of 35 write-in votes.
Although it may sound trivial to require even 35 write-in votes, many New Hampshire State House districts are very small. The state has 400 State House members, and in some districts that only a single member, fewer than 1,000 voters may turn out at the primary.