When talking about accidents, there are basically two different scenarios:
In either case, check what your accident insurance policy offer. Based on your own understanding, cycling style and etc, you should decide which accident insurance level suit your own needs.
Like in any other accident insurance, If you've been injured, you get paid out up to a certain amount of money. There is also an amount paid to the family in a case of death and a different amount that is paid if the injury caused the rider to become handicapped.
If you injure someone or damage their property while cycling, you may need to deal with a claim for compensation. In this case, you will need a third party insurance that will cover the expenses.
Bicycles and in particular electric bicycles are pretty fast vehicles. They are not as fast as cars and motorcycles (and weigh much less) of course and that is the reason why you can use them legally on streets, parks and etc. Nevertheless, hitting someone at a speed of 25km/h can cause severe injuries.
The feeling a pedestrian has when a bicycle is heading toward him is somewhat similar to the feeling that a cyclist have when a car is heading toward him.
Ideally, pedestrians, heavy vehicles and light vehicles (such as e-bikes) should not share the same territory. Each should has it's on lanes/streets. In most countries and cities, this is far from true and so you need to think about a 3rd party insurances seriously.
If you insure you bike, check what are the conditions. Does anyone can ride the bike or only you? Does a child can ride it or is there any age limit?
A nice addition to any insurance policy is a cyclist rescue option. If you are an avid cyclists, it can really suit you.
If for some reason, you are unable to complete your trip, you can use this service to assist you.
Some kind of a transportation vehicle will be sent to you and carry you and your bike to your car, nearest train station, cycle repair shop or any other place following your request (of course, under the policy conditions).
You should be able to use this service if your bike has been stolen, after an accident, had some sort of vandalism or mechanical breakdown.
Check under what condition you deserve to be treated. Also, if it's important to you, check the promised average response time.
Overseas accident insurance is usually a whole different story, check what the insurance policy can offer you if you are traveling a lot with your e-bike.
For the really spoiled one among of you or for those who afraid of punctures (having more punctures then punctures kits), check for availability of a puncture rescue option.