Dodd was born in Norwich, New London County, to Abigail Margaret (née O'Sullivan) and Thomas Joseph Dodd, a building contractor; all four of his grandparents were immigrants from Ireland.
Dodd became vice chairman of the Board of Review and later executive trial counsel for the Office of the United States Chief of Counsel for the Prosecution of Axis Criminality at Nuremberg, Germany, in 1945 and 1946.