Heather Nova's cover of John Lennon's "Norwegian Wood" premiered February 18, 2012 on the "BBC Radio Merseyside" show "On the best". The song will be also on a John Lennon tribute album, to be released June 21, 2012.
You can listen to the BBC show on the John Lennon tribute album website. Right at the bottom there is the player.
The 38 minutes broadcast contains the song (at the beginning) and an interview with Bermudian Tony Brennan, the executive producer, about the John Lennon tribute album and about John Lennon itself.