I would think it depends on the laws of the country where the trial will be performed. If you plan a clinical trial you'd better read the law or have a lawyer interpreting it for you.
According to David Neal, National Research Ethics Service (NRES) in the UK, "an EU-wide legislation for insurance for clinical trial participants is not possible due to significant variations the affiliated countries". So I share the opinion of Pierluigi that one has to check the given conditions and laws of the initiating country.
Also, it will depend on the design of the project.
If it is a retrospective study, you would not need an insurance, but
If it is an interventionist clinical trial, you will need it: If you have planned to apply the routine medical practice to all patients, maybe, you can be covered by your professional insurance. But, if you randomize the patients for to be treated or not, by changing their lifestyle or any other treatment, you would need it.
As you have to present the project to an EC for its approval, they will ask for it if proceeds. However, is better to be informed about the laws of the country, as have
On the assumption that this will be a prospective study you should first get appropriate approval from a research ethics committee and an independent scientific review may also be needed in some centres (attitudes to the latter vary within countries). Funding agencies may require both. Your potential problems may arise from issues of confidentiality as well as from the interventions themselves and the risk implications of these hazards depend very much on the protocol and on the experience of the investigators. Therefore I agree that professional and public liability insurance is needed. It would probably be to your advantage to consider having an independent separate steering committee with appropriate expertise, and an Independent Data Monitoring Committee. All these are evidence that science and research is becoming increasingly professional and the roles of these entities are described in the major biomedical journals. I presume that most Institutes, Health Providers, companies involved with Health products, and Academic centres have a general insurance coverage which would help you. However, if you do not have access to such cover, there seems to be limited expertise amongst Insurance Companies and Brokers to cover biomedical research, and you will need to get local expertise to help you find one.