If you are checking on a specific property by address you can check the town tax card, they list sales. Also,
www.nhdeeds.com can be searched by name of either the buyer or seller. If you look at the tax stamp on the deed and do the calculation you can figure out a sale price.
I believe there is a publication that is put out that lists all real esate transactions but can't think of the name of it. They usually will be in the paper as well.