Private civil liability and household contents insurances are not mandatory, but in Switzerland most of the lessors will demand it against potential damage.
Private civil liability
Private civil liability insurance allows covering you against financial consequences of damage which you cause to others.
Household contents insurance
Household contents insurance allows covering your household contents in case of fire, natural damages, theft and water damages. According to your needs, you can add options as glass building insurance, all risk (electronic damages), etc…