The Clovis News Journal ( http://bit.ly/1aEsll1) reports the kitten apparently had taken refuge for the night in a shed at the site at Ute Lake.
When workers arrived Monday morning, the kitten ran out and scampered away.
Workers later began hearing meows and then spotted the kitten at the bottom of the shaft.
Project engineer Mitch Haskins says a worker descended to the bottom of the shaft, returning to the surface with the kitten in hand. It was frightened but appeared to not have visible physical injuries.
Haskin says the works decided to call the kitten "Petty" after Tom Petty, the singer of ''Free Fallin."