Unfortunately your picture doesn't give a good sense of scale, but my first reaction was that it looked like dog poop. Some other canid is also possible, with coyote being the most probable, then fox.
As for safety concert, you don't need to examine poop for that. There is nothing in southern NH that is a physical threat to humans, at least assuming a normal healthy animal. Black bears can hurt you if they want to, but they don't want to, unless you do something deliberately stupid. The most dangerous animal in NH is a human. Second on the list is a moose. But again, other than humans, nothing is going to bother you unless you do something stupid.
I hike around a lot in nothern MA and sometimes in the White Mountains of NH, and I have never come accross any animal that presented a danger. We have coyotes living in the woods around our house in northern MA, but they present no danger. They run away as soon as they see us. Actually we see them only occasionally, but we hear them howling every night in response to nearby train whistles.