It has been five years since a former curator of the J. Paul Getty Museum in Los Angeles went on trial in Rome for conspiring to traffic in stolen antiquities. The case has become a cornerstone of Italy’s aggressive campaign to recover ancient treasures from around the United States and has led major American museums to make their peace with the Italian government. As the museums have relinquished dozens of artworks that Italy claims were looted, receiving loans of other objects in exchange, officials on both sides have talked about a new era of collaboration.

But now an Italian investigation of a second American museum curator, in a case involving similar allegations of criminal conspiracy, seems likely to upend assumptions about any rapprochement. According to a 14-page legal notice from the public prosecutor’s office in Rome, J. Michael Padgett, 56, antiquities curator at the Princeton University Museum of Art, is a focus of a criminal investigation of “the illegal export and laundering” of Italian archaeological objects.

Once again an American may be facing a drawn-out legal ordeal, and at least the hypothetical threat of incarceration in a foreign country, for acquiring art for a museum — something that was unheard of before the Getty case, and that many museum professionals believed was not going to happen again....