A Greenwich doctor who is a registered sex offender in Connecticut and New York was denied a hearing Tuesday on his request to have his Connecticut medical license reinstated. The state Medical Examining Board – which alarmed some patient advocates in 2011 when it voted to allow Dr. Clifford A. Berken to practice with some restrictions following his arrest on sex charges – denied the request from Berken and his attorney Diana Carlino. The state Department of Public Health had objected to giving him a hearing. Berken, a doctor of internal medicine and gastroenterology, had surrendered his medical privileges at Greenwich Hospital and left his private practice in Greenwich, following his arrest in New York in 2008. In 2010, Berken pleaded guilty to charges by the Westchester County District Attorney’s Office in New York that he had engaged in sexually explicit online conversations with an undercover officer posing as a 15-year-old boy.