If you just arrived and are planning to stay for a few years or less, and want to keep your old health insurance, here is how you can get out of the Swiss one.

Download the form at your kanton that is based on bilateral EU exclusions, have your own insurance sign it, and then personally take it to your kanton's office. This is the hard way as not all companies sign it and not all kantons accept the signed form.

The easy way for EU citizens that can get a European Health Insurance Card is that you just show it to the same appropriate kanton's office. Under these bilateral rules, they should except the card as proof and not bother with the form.

If you have EU insurance, ask them about the card if you do not have one yet. It looks like a credit card with policy nr /name on it and the other side has the EU logo of stars in a circle.