This link is helpful: https://travel.state.gov/content/travel/en/legal/travel-legal-considerations/Advice-about-Possible-Loss-of-US-Nationality-Dual-Nationality/Dual-Nationality.html
"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 to travel to or from a country other than the United States is not inconsistent with U.S. law."