All drones other than CE-marked toys must be insured in accordance with (EC) No 758/2004. That means you need to have third-party liability insurance covering at least 0.75 million SDRs (ca. 9.2 million NOK per 31.12.2020).
In Norway, all aircraft that weigh less than 500 kg must be insured for at least 750 000 SDR (about 9,5 million NOK as of December 12, 2020). This is according to regulation Forskrift om minstestørrelser på forsikringssummer for passasjer- og tredjemannsansvaret § 4.
This means that you have to have liability insurance for your drone since the new regulations define all types of drones and model airplanes as unmanned aircraft. The only exemption is for drones that are CE-marked as toys in accordance with directive 2009/48/EF. The requirement for insurance is rooted inn regulation Forskrift om luftfart med ubemannet luftfartøy i åpen- og i spesifikk kategori § 7.
The requirement for insurance is based on the fact that the owner of an aircraft is liable for any damage that may occur under flight conditions, regardless of guilt. This is rooted in air law: luftfartsloven § 11-1.