Yes, our State Department “recognizes “ that some US citizens have dual nationalities but it has no legal status with them. The major problem for US citizens holding citizenship in another country arises if/when they travel abroad with a non-US passport. A former co-worker of mine had dual US-Italian citizenship. He got into a minor legal scrape while visiting Italy on his Italian passport. The US consulate wouldn’t help him because he had not entered the country on a US passport. Another problem is if a dual national leaves the US on, say, an Italian passport and tries to re-enter on a US passport. That does not make the US authorities happy, to say the least. My friend’s advice, learned by him the hard way, is always travel to and from the US with your US passport, regardless of your dual citizenship.
A U.S. national may acquire foreign nationality by marriage, or a person naturalized as a U.S. national may not lose the nationality of the country of birth. U.S. law does not mention dual nationality or require a person to choose one nationality or another. Also, a person who is automatically granted another nationality does not risk losing U.S. nationality. However, a person who acquires a foreign nationality by applying for it may lose U.S. nationality. In order to lose U.S. nationality, the law requires that the person must apply for the foreign nationality voluntarily, by free choice, and with the intention to give up U.S. nationality.
Intent can be shown by the person's statements or conduct. The U.S. Government recognizes that dual nationality exists but does not encourage it as a matter of policy because of the problems it may cause. Claims of other countries on dual national U.S. nationals may conflict with U.S. law, and dual nationality may limit U.S. Government efforts to assist nationals abroad. The country where a dual national is located generally has a stronger claim to that person's allegiance.
However, dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there. Most U.S. nationals, including dual nationals, must use a U.S. passport to enter and leave the United States. Dual nationals may also be required by the foreign country to use its passport to enter and leave that country. Use of the foreign passport does not endanger U.S. nationality. Most countries permit a person to renounce or otherwise lose nationality.