As Jeani K. mentioned, the Stadthaus is where the 'welcome to ZH' events (one for Germans & one for…read morethe rest of us) are located. For those of us on the 'other end' of our CH experience, the Stadthaus is also where one 'de-registers' from Swiss life.
One brings one's Kreisbüro ID along with formal ID to one of few 'Abmeldung' lines located on the ground floor to start the ball rolling. Be prepared to be sent to a couple different offices during the Abmeldung process. The first office deals with taxes. If one hasn't yet paid taxes before exiting CH, then that transaction will take place then and there. The last stop was to obtain an official paper showing that one will be leaving the country and it is used to cancel insurance, phone service, etc.
De-registering sets one back 30 CHF per person. Cash or card accepted.
We had absolutely no issues with our Abmeldung process. Staff were professional and helpful. It's nice to have a smooth send off!