It depends on the State. Each state in the US has it's own rules regarding divorcing in that state. Often there is a residency requirement. As long as you fulfill that state residency requirement, you can diorce in the USA no matter where you were married. Also, the fact that you were married in CH does not mean that you have to get divorced in CH. You can get divorced in any country as long as you fulfill all the conditions of that country, and regardless of you nationality (ties). Due to international laws, if your spouse were to ask for a divorce first in CH, then a US court may not have juisdiction to hear your divorce petition. So in order to divorce in the USA, there must also not be a divorce case pending in CH.
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