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Driving on public roads requires you to have third party insurance.
Any motor vehicle driven on public highways must be covered by third party liability insurance. This covers the vehicle owner and persons for whom the owner is responsible under the Road Traffic Act in the event of damage caused to third parties, i.e. any driver of the insured vehicle who causes the damage through negligence, and any persons assisting the driver who have also acted negligently. This scenario may arise, for example, if the driver requests a person to guide him/her out of a blind exit. Check the terms and conditions of your insurance policy.
You are insured for personal liability in all countries in which the Swiss number plate counts as proof of insurance (currently all EU/EEA states, Andorra, Serbia and Switzerland).
Damage to your own vehicle is not covered by third party insurance. You can take out an additional policy to cover your own vehicle.
Internet comparison sites can help you to find the best insurance policy for your needs.