This is difficult to answer. More and more computer systems are being connected and there is always the possibility while entering the US that questions on your tax status could be asked.
Traveling into the US on your other nationality passport (if you have one) is not allowed:
According to Section 215 of the U.S. Immigration and Nationality Act (8 U.S.C. 1185), it is illegal for an American citizen to enter or leave the US on anything other than an American passport. This applies to dual citizens as well. Meaning that persons holding both American and another country’s citizenship must enter and depart from the US on a valid US passport. This applies to children as well as adults.