 Despite his lack of formal legal training, Davenport was appointed judge of the Fairfield County Court, the Maritime Court of Fairfield County, and Stamford's probate court (from 1768–1790).In his waning years, Davenport served as the chief justice of the Connecticut Court of Common Pleas.The judge was in Danbury, Connecticut hearing a case when he suffered a myocardial infarction.