He was in private practice of law in New London, Connecticut from 1905 to 1906.

[1] Burrows was nominated by President Calvin Coolidge on February 3, 1928, to the United States District Court for the District of Connecticut, to a new seat authorized by 44 Stat.

He was confirmed by the United States Senate on February 16, 1928, and received his commission the same day.

His service terminated on October 20, 1930, due to his resignation.

[1] Following his resignation from the federal bench, Burrows served as the 8th Attorney General of Connecticut from 1931 to 1935.