This Albany Times-Union story explains that the Reform Party is letting independents vote in its primaries on September 12. It imples that this has never happened before in New York, although some years ago there were some Independence Party primaries for district and local office that also permitted independents to vote. Thanks to several people for the link.
A petition to designate a candidate for nomination requires 5% of the enrolled party members. The same number is needed for an Opportunity To Ballot (OTB)
New York always permits write-ins in primaries, but it cancels the primary if it is uncontested. If an Opportunity To Ballot petition is circulated, then the primary is always considered contested. In some cases there will be no on-ballot candidates, and the winner will be determined by write-ins. In other cases, the OTB will force an unopposed candidate to defeat write-in candidates.
Rensselaer County, the subject of the article, has multi-member districts for the county legislature. In some districts for the Reform Primary, there are no on-ballot candidates. 5% of the Reform enrollees is 1 (one). So one voter was able to trigger an OTB, and independent voters who vote the Reform ballot will be able to write in anybody, whether on-ballot candidates for other parties, or themselves, or a friend.