Answer: What fun!
While Corylus avellana is one of the species grown for edible nut production, finding nuts on "Contorta" is extremely rare. (You may be able to harvest them if you can beat the squirrels this fall!)
Here is what I suspect has happened. It is possible that your ornamental plant was grafted to a non-ornamental root stock. If that root stock has managed to send up a sucker or branch, it could fruit. This would explain why only one branch has nuts on it. Take a very close look at your shrub and see if you can tell if this is what happened.
In the meantime, enjoy your crop!
Q&A Library Searching Tips