Mayor Bill de Blasio’s former press secretary Karen Hinton was placed in a medically induced coma over the weekend after suffering a head injury, a relative said Monday. Hinton, 58, got lightheaded while running on a treadmill and fell, injuring her head, Hamilton Hinton, her nephew, told The Post. She had bleeding on the brain and doctors placed her in a coma, said her nephew, who lives in Hinton’s native Mississippi.