The house in front dates from about 1880. The lots in this area were developed from the late 1860s on, by the selling off of the Pierpont Foster Estate (information from the New Haven Historic Inventory - various entries from Foster and Avon Streets). I don't know whether this barn was built on the estate prior to subdivision, or built with this house. Whitney Avenue National Register Historic District.
Devlin, William E. and Clouette, Bruce, Whitney Avenue Historic District National Register Nomination No. 88003209, National Park Services, 1988.