Certainly! Go to the BN app store and download the app Overdrive for free. It will let you check out public library ebooks from your nook. You have to have a library card of course, and you have to have a free Adobe ID from adobe.com to enter into Overdrive before you can download anything. Be sure you only check out Adobe *.epub file formats from your library. The books will last about 3 weeks and then poof away.
Have a Nook HD and enjoy B&N offerings but would occasionally like to be able to download an e-book from local library. Is this possible?
There is also the "other" alternative. If you have the Kindle app on your HD, choose the K book on the library page and when the Amazon page pulls up, choose "send to Michael's Android tablet" on the dropdown menu.