The place you are looking for is New Britain, Vermont. It is located in the southern part of the state near Brattleboro, to the best of my memory. Any information on Vermont families must be obtained from each individual town clerk's office for that town. You would need to contact the town clerk of New Britain for any information.
I was born in Vermont as was the majority of my ancestors. I just made a three week vigil to the state, going from town clerks office to town clerks office to obtain vital records. Vital records can be ordered. Each town clerk has their own way of doing this.