To answer the question directly, it is not nece

To answer the question directly, it is not necessary for you to relinquish your citizenship or even get a dual citizenship in order to live in Panama. You can be a perpetual tourist, if you follow the rules, or you can get one of the different visas available.
When you come to Panama, you can come as a tourist or a visitor, and stay for 180 days, but then you have to leave the country for 72 hours. Then you can come back again. There are people who are stay in Panama indefinitely as perpetual tourists.
By law a Pensionado in Panama does not need a passport and possible Panamanian citizenship, but the government of Panama recently changed that rule, so that now, after a person’s has legally been here for five years, you can apply for citizenship. Nobody that I know has ever become a citizen and received a Panamanian passport that I know of, though, so it is absolutely not necessary in order to stay in Panama.
There are programs like the one they have in Saint Kitts, where you could start with an investment of US $350,000 and receive citizenship. To renounce your citizenship is a gray area. You may want to renounce your citizenship or you may not.
I know a Canadian guy who says that he has done everything to become a citizen of Panama, but the president of Panama needs to approve his application to become a citizen. That is the only thing he is says he needs, and I am waiting to see if that happens.
I am a US citizen and because I am a US citizen living overseas, I have to put up with some crazy laws. Because I am a citizen of the United States, I have to send in a report to Detroit telling the government what money I have in foreign bank accounts, and if I do not tell them, the penalty is 50% per year. So just because you already live in another country, does not relieve you of taxes and some other legal obligations in the US, because you are still a US citizen.

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