A 47-year-old man visiting the park from Schenectady, N.Y., was also taken to a local hospital for a back injury he suffered as he tried to catch the girl, police said.
The police investigation into the exact circumstances surrounding the fall is continuing.
The Sheriff's Office did not say what the girl was doing and how she ended up hanging from the ride in the first place.
Onlookers erupted in applause when she landed safely. A 14-year-old girl was left dangling 25 feet above them while her brother held onto her shirt for dear life.
"Looking at her today and knowing she was alright because of me and my daughter made it worth it".
The girl was taken to the hospital but sustained no serious injuries.
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Warren County sheriff's Lt. Steven Stockdale said "human error" by the teenager caused her to slip under the metal safety bar, The Post-Star of Glen Falls reported. He expected to release additional information later Tuesday.
"Let your legs dangle in the air as you board your open, two-person cable vehicle in Fest Area", the website said.
The ride was shut down for the remainder of the day and inspected for any technical malfunctions but appeared to be in working order. "It wouldn't surprise me at all if they put additional safety restrictions on this ride, maybe safety belts".
The girl was riding the attraction with a younger relative. The ride was stopped by an operator after getting word of a rider in distress - it had been higher up at one point, according to the Associated Press.
Howard told the girl to fall and promised he'd catch her.