The car's 21-year-old driver was released following a routine blood-alcohol test, police said.
Public Safety Director Troy Riggs said McCormick's death is the first known line-of-duty death of an emergency services worker in the city's history. He said medics, police and firefighters are a family.
"Today a member of that family is missing," Riggs said. He said McCormick's death will be handled like that of a police officer or firefighter.
Indianapolis Mayor Greg Ballard said in a statement that McCormick's death was "a terrible loss."
"When we are most in need, IEMS takes care of us. Now it is our time as a community to take care of them," he said.