The autonomous region is an integral part of the European Union, having pronounced status as an outermost region of the European Union, as detailed in Article 299-2 of the Treaty of the European Union.
Madeira was claimed by Portuguese sailors in the service of Prince Henry the Navigator in 1419 and settled after 1420.
Police located the body by using ground-penetrating radar on land next to Miss Khan's home.
An autopsy is said to have shown no signs of violence.
The archipelago is just under 400 kilometres (250 mi) north of Tenerife, Canary Islands.