There are mountain lions in NH - don't doubt it - and a sighting here in Alton not too long ago by our neighbor. We have a stream that runs down Route 140 and borders several home-owners' property lines in our area. It sorta pools up behind my neighbors' house (Cats In The Cradle Soap) and they get a plethora of wildlife back there - beavers, bears, and mountain lions! 
And bears are out now - I hear one "oof!"ing (that whispery-bark they do) the other night when I took the dog out... couldn't get back in the house fast enough thankyouverymuch!