As the subtenant, you are responsible towards your landlord for the apartment and furnishing. For this reason, it is important that you arrange a personal liability insurance which covers the liability for possible damages done to the rental property in Switzerland. In the Western part of Switzerland there are regulations saying that all tenants need to arrange a private liability insurance.
A personal liability insurance is low cost coverage for damages caused by those accidents which so easily happen in everyday life. The insurance only costs approx. CHF 100.- per year (for a family approx. CHF 150.-) and can be arranged with any swiss insurance company.