Boston Marathon bombings suspect's condition improves Updated at 3:57 p.m. BOSTONFederal officials say the Boston Marathon bombing suspect's medical condition has improved. Boston bombing suspect charged at hospital bedside Dzhokhar Tsarnaev remains hospitalized under heavy guard. He is being treated at Boston's Beth Israel Deaconess Medical Center, where 11 victims of the bombing were still hospitalized. He had been listed in serious condition at a Boston hospital since he was captured Friday night after an intense all-day manhunt that brought the Boston area to a near-standstill. The 19-year-old was wounded in a shootout with police and suffered gunshot wounds in the head, neck, legs and hand. Officials say Tsarnaev is recuperating from a bullet wound in the leg and in the neck. They could not comment on whether or not the neck wound was self-inflicted. CBS News correspondent Bob Orr reports that Tsarnaev is cooperating with authorities, who have not found any evidence of ties to major terror organizations. Injured from a gunshot wound to the neck that has rendered him unable to speak, he is communicating via writing. On Tuesday, the U.S. attorney's office said his condition had been upgraded to fair. Tsarnaev was charged Monday in the twin bombings that killed three people and wounded more than 260. His older brother, Tamerlan Tsarnaev, was killed during the shootout.