Zip Code 06756 Unacceptable Postal Names. 06756 is located in the state of Connecticut in the Hartford-New Haven metro area. Zip code 06756 is primarily located in Litchfield County. The official postal service name used for 06756 is GOSHEN, Connecticut.Portions of the 06756 zip code are contained within or border the city limits of Torrington, CT, .6756 is located in the state of Connecticut in the Hartford-New Haven metro area. Zip code 06756 is primarily located in Litchfield County. The official postal service name used for 06756 is GOSHEN, Connecticut. Portions of the 06756 zip code are contained within or border the city limits of Torrington, CT, .