The Federal Accident Insurance Act (UVG) applies to accident insurance offered both by private insurers and by SUVA.
The premiums for insurance covering occupational accidents and illnesses must be paid by the employer. The premiums for non-occupational accidents must generally be paid by the employees themselves. The employer pays the full premium and then deducts the share for non-occupational accidents from the employee's salary.
UVG accident insurance covers treatment costs in case of occupational and non-occupational accidents, i.e. also those occurring during your time off. If you work for the same employer for at least 8 hours per week, you automatically receive accident insurance (according to UVG) through that employer – and can therefore take out health insurance without accident cover without hesitation. Depending on the insurance company, this results in a premium reduction of up to 10%. You must notify your provider as soon as you are no longer insured against accidents through your employer. Accident cover according to the Health Insurance Act (KVG) then comes into effect with a resulting rise in premiums. Those receiving unemployment benefits are insured from SUVA against accidents.
Note: accident coverage from an employer-provided insurance (UVG) offers much better protection than accident insurance taken out in conjunction with basic insurance (KVG). Benefits covered by UVG accident insurance are not subject to a deductible or coinsurance. There are also additional benefits in case of serious accidents such as a daily allowance for salary loss, disability and survivor's pensions, integrity and attendance allowances and partial payment of funeral costs.
You can find the legal text here (text not available in English).