Norwegian financial institutions are obliged to record information about customers who are resident abroad for tax purposes when a new account is set up. They must do this by gathering statutory information from you as a customer.
Financial institutions are also required to review information concerning existing customers in order to identify any information that may indicate that the customer concerned is resident abroad for tax purposes. If a financial institution finds such information about you, it must in the first instance treat your accounts as belonging to a foreign customer when submitting annual reports to the Norwegian Tax Administration. The financial institution must contact you to ask you to provide a foreign identification number if you are affiliated to a country that issues relevant identification numbers. The financial institution must not treat your accounts in this way if you provide information/documentation demonstrating that you are not resident for tax purposes in the country concerned.
The rules of the country concerned will determine whether you are resident for tax purposes there. The fact that information is sent abroad does not alter this situation, but the information may result in the foreign tax authorities becoming aware of your accounts in Norway.
The Norwegian Tax Administration has published guidelines explaining the obligations of financial institutions. You will find these guidelines here.