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| Can a EU-resident be employed by a Swiss company without the person having to move to Switzerland? | |
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Yes. This is not a problem at all. Plenty of French and Germans do this (frontaliers / Grenzgänger). Plenty of Swiss do this, being sent abroad for, e.g., project work.
Note that nationality does not matter - country of residence does.
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| If so, how does the taxation work? | |
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The driving factors here are where you perform your work and where you live.
From the tone of your question it appears as if you would be performing work outside of Switzerland and, obviously, not live in Switzerland. In this case, you will most likely be taxed by your country of residence, with a small share of the(se) taxes going to Switzerland. The details will most likely be spelled out in a double taxation treaty between Switzerland and the country of your residence.
Independent of taxation, your employment would make you subject to the social security system of Switzerland - i.e. you would switch into the Swiss health insurance system ("Obligatorische Krankenpflegeversicherung EU/EFTA (KVG)"), pay unemployment insurance contribution, and also join the Swiss pension system (the contributions to which you may withdraw in part once your employment contract with the Swiss company has ended).