The people living in ZIP code 06770 are primarily white. State: Connecticut Zip Codes. ZIP Code: Type: County: Population: Area Code(s) ZIP Code 06770: Standard: New Haven: 31,975: 203 / 475 ZIP code: 06770. For Season Recreational Or Occasional Use. ZIP Code 06770 is in the following school districts: Naugatuck School District and Private. Find MoreCities in Connecticut that start with N, Post Office Suburb:NAUGATUCK, CT, 06770-9998,