Nick Broomfield’s “Kurt and Courtney” will make its New York premiere May 29 at the first annual New York Intl. Documentary Festival.The controversial docu about the marriage of Courtney Love and the late rocker Kurt Cobain will screen at midnight at the Directors Guild of America Theater. The docfest began Wednesday night and continues through Sunday. In addition to “Kurt and Courtney,” 16 new and classics docus will unspool at the fest. Tickets are $8 per screening. A festival pass is $60. For more information, call the hotline at (212) 668-1575 or visit the Web site at http://www.docfest.org.