notify them both
you will have to notify both the service center and your local office of any change of adress
by the way i am applying to the same service center ,
beside the application and the fees for the application and the fingerprint did you send any other documents
mine is based on 5 year continuous residency ,i am married but she still waiting overseas(i applied i 130)recently .
do i need any other document to send with my N 400 ???
your help will be appreciated ,god bless