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Any adult person can open an account at a bank in Switzerland. However, the legal provisions of Switzerland with regard to cross border business have to be respected. Banks reserve furthermore the right to reject customers. http://www.swissbanking.org/en/faq#sthash.2HwvE8QF.dpuf
If you are a U.S. citizen and you have a foreign bank account, you will have a reporting requirement to the IRS via FBAR if there is $10,000 at any time during the calendar year in the account. http://www.irs.gov/Businesses/Comparison-of-Form-8938-and-FBAR-Requirements
Also, as a U.S. citizen you are required to report your worldwide income, so the interest earned on the money in the Swiss bank account will be reported on your U.S. tax return.
If you are planning to rent the flat, the income (and expenses) will be reported on your U.S. tax return. If and when you sell the flat, you will report the sale and pay tax on any capital gains realized from the sale in the U.S. and Switzerland.
There is a Tax Treaty in place between the U.S. and Switzerland which provides for relief from double taxation. In other words, if you are a resident of the U.S., you would receive a credit for any taxes paid to Switzerland. Please refer specifically to Articles 6, 11, 13 and 23 of the Tax Treaty.
I realize this is a great deal of information, but once you have had an opportunity to review it, please come back to me here at your convenience if you have any other questions or concerns.
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