No, the murder of Stacey Burns is not among the over 100 murder cases mentioned in a post from WMUR-TV in Manchester. I guess that should make everyone feel much better, although the list they have has not been updated since mid-2012. Perhaps in the last year and an half her case has been moved into that category but that does not appear to be the case.
Google unsolved murders in New Hampshire and you will have many informative articles to read, but be prepared to be depressed. Think about it: if the list of unsolved murders is even half correct, there are at least fifty killers who have literally gotten away with murder in the state. If it is completely correct, over one hundred murderers have never been caught!