An Amagansett man who told police he had been mugged ended up on Jan. 4 with a charge of falsely reporting a crime. Agustin Barranco Reyes, 48, went to East Hampton Village police headquarters that afternoon and reported that he had just parked in the Reutershan lot near Latin Express when a man came up behind him, put him in a chokehold, and pulled his wallet out of his rear pants pocket. Mr. Reyes told police he had his identification and $50 in the wallet. The Reutershan lot is covered by surveillance cameras, and police immediately brought up the appropriate video. They said it showed Mr. Reyes driving into the lot, parking, then driving away without ever getting out of the car. Confronted with the video, police said Mr. Reyes confessed that he had made the story up. He had lost the wallet in mid-December, he admitted. Charged with the misdemeanor, he was released from headquarters after posting $500 bail. He will be arraigned on Feb. 4 in East Hampton Town Justice Court.