When it is time to 'de-register' from life in La Suisse, then one must go directly to the Stadthaus/City Hall and not to the Kreisbüro as I had originally thought. Had I actually read the print on the small 'district ID' that comes with living in a particular area, then I would have known. It states clearly that one must visit the Stadthaus for 'de-registration'. What could be clearer? Once at the Stadthaus, proceed directly to the windows marked 'Abmeldung'. They are located on the ground floor to the right of the entrance. There one may encounter orderly lines or a cluster of people all jockeying for position. Do not be deterred. Have both the Kreisbüro ID and formal ID at the ready. Once processed, one is sent to a tax office. All unpaid taxes must then be paid. After that, one returns to the initial intake person, for what exactly I don't know, then one is sent to the final office. It is there one receives the very important piece of paper showing one is to leave CH. With this paper, and, I am told, this paper alone, one is able to cancel insurance policies, phone contracts, etc.
The whole affair lasted around 20 minutes. We were dealt with in a professional and courteous manner. It's not easy shutting one's life down and moving country. At least the process of 'de-registration' was easy-peasy.