A police officer died after he was shot in the head while chasing a gunman in East Harlem on Tuesday, Police Commissioner William J. Bratton said. The officer was shot around 8:30 p.m. near Franklin D. Roosevelt Drive and 120th Street, the police said. He had been responding to an armed robbery in a park when the chase began, police officials said. The officer, identified as Randolph Holder, 33, was taken in critical condition to Harlem Hospital, where he died a few hours later, the police said.