Liechtenstein is not in the European Union, that's because you need a residence permit. For applying for this permit you need to contact the local authority. On their website you find a lot of information about the different types of authorization:
Ausländer- und Passamt
Tel. +423 / 236 61 41
Fax +423 / 236 61 66
After you got the residence permit you need a residential permit, which you get at the community where you live.
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