In order to obtain a residence permit, it is obligatory to have adequate health insurance. Probably the best way to proceed is to first have prove that initially you are still covered by the health insurance from the country you are emigrating from, and then get a local health insurance. The reason is that sometimes a Dutch insurance company requires you to have a residence permit, which however, the authorities will only provide if you are covered by health insurance.
Most national health insurance packages within the EU are valid in The Netherlands. To prove this, ask your health insurance company for a form called an E111 or E112. If necessary you can arrange medical insurance upon arrival.
Third-party liability insurance is compulsory in The Netherlands. This insurance protects you in the event of you causing damage to someone else or to someone else's possessions (for example, if you cause a traffic accident with your bike or as a pedestrian).
Leiden University can provide a combined insurance policy (health and third-party liability). Contact the personnel department for more information.