Carlsbad Mayor Bob Forrest said he doesn't know for certain if he or his twin brother, Dick Forrest, fired the shot during the hunting trip in the late 1990s. It accidentally pelted Cheney, who was then chief executive at Halliburton Co.
"We're probably the only twins in the United States that have shot the vice president and never have gone to jail," Forrest joked. The Albuquerque Journal reported the incident Sunday.
Cheney wasn't hurt but he was miffed, Forrest told the Journal.
"He said, 'You guys watch where you're shooting!' He was very offended," Forrest said.
The hunting group included the Forrest twins, Cheney and Sen. Pete Domenici, R-N.M. They were hunting on a southern New Mexico ranch owned by the late Colin McMillan, an assistant secretary of defense under President George H.W. Bush, Forrest said. He said the senator wasn't the shooter.
A spokesman for Domenici confirmed that the senator hunts with the Forrest brothers and has hunted with Cheney but declined further comment.
A message left Monday with Cheney's office seeking comment was not immediately returned to The Associated Press. The Journal said several phone calls to Cheney's office last week also were not returned.
Cheney, during a Feb. 11 hunting trip in Texas, Cheney accidentally peppered lawyer Harry Whittington in the torso, neck and face with up to 200 shotgun pellets.
Whittington sustained a mild heart attack caused by a pellet lodged near his heart three days after the shooting. He has since been released from a hospital. Kenedy County, Texas, Sheriff Ramon Salinas ruled the shooting an accident.