Capt. Ronald Smith of the Hamden Police Department said authorities responded to a Hamden address Monday and firefighters attempted CPR, but Legesse was pronounced dead at Yale-New Haven Hospital, The Hartford (Conn.) Courant reported Thursday.
Doctors were able to deliver the baby, a daughter.
Legesse was 17 when she competed in the 1,500 meter run at the 2004 Olympics, where she placed 17th.
Bill Staab, president of the West Side Runners club, based in New York, said he knew Legesse, but she was not a member of the club.
"She was quite beloved in the running community," Staab said. "She was charming, a very attractive woman and a good mother. It's a tremendous loss to the Ethiopian running community in the New York area."
Legesse is survived by her newborn daughter, a 2-year-old son and her husband, Tom Laverty.