New Hampshire refers to unclaimed money as abandoned money. The site notes $6.3 million was returned last year to 10,800 claimants. Their site has an FAQ section for general questions on unclaimed funds, a link page to other unclaimed sources, and guidelines for holders.
State of New Hampshire Treasury
25 Capitol Street, Room 121
Concord, NH 03301
Phone: (800) 791-0920 (in New Hampshire) (603) 271-2619 (out of state)