A pile of goat manure spontaneously caught fire, spreading a stench and wrinkling noses through a Vermont town but causing no damage, officials said. The odor evoked ‘‘a damp kind of burning leaves or brush fire,’’ Windsor Town Manager Tom Marsh said. A worker on her way to milk goats discovered the fire in the 120-cubic-yard manure pile at about 3 a.m. Wednesday, said George Redick, owner of Oak Knoll Dairy, which has 800 goats. Redick and others put out the flames with water from a hose but the pile continued to smolder. Marsh said he could smell the fire at his hilltop home 5 miles away. He called it ‘‘a little disconcerting, because it was a very strong smell.’’ Redick said he used to think spontaneous combustion was make-believe. ‘‘Now I’m a believer,’’ he said.