Giuseppe Profiti, former hospital president, and Massimo Spina, the former treasurer, are under investigation, said Greg Burke, assistant director of the Vatican press office.
Bertone, former Vatican secretary of state, is not under investigation, Burke told reporters March 31.
Profiti resigned in January 2015 amid rumours that a significant amount of money from the foundation supporting the child's hospital was used to help finance the remodelling of Bertone's Vatican apartment.
Mariella Enoc, current hospital president, told reporters in late December, "Cardinal Bertone never directly received money (from the hospital's foundation), but recognized that we suffered a loss and, therefore, assisted us with a donation of 150,000 euros," about $220,000.
Emiliano Fittipaldi, a journalist currently on trial at the Vatican for publishing allegedly stolen Vatican documents, wrote in the Italian magazine Espresso March 31 that the total cost of combining and remodelling two apartments was almost $620,000. Bertone has repeatedly disputed news reports about the size of the apartment and its cost, and he has insisted that he personally paid the Vatican, which owns the apartment, for the work done.