Robertson is the sole trustee in a trust with an energy company subsidiary CENCO Inc., which it sold in 2004.
While it was still owned by the trust, CENCO purchased an idle California refinery in 1998, the Norfolk, Va., Virginian-Pilot reported Tuesday.
The bank originally filed suit against the trust, then added Robertson as a defendant in March, seeking $3.6 million it says it is owed in payments on the credit agreement, plus fees and interest charges.
The bank also claims the trust failed to keep $11.4 million available as part of the agreement.
Robertson is counter-suing for $4 million, claiming the credit agreement was intended to shield the trust from certain liabilities, the newspaper said.
Federal Judge Jerome Friedmann has already denied a petition from Robertson to have the suit against him dismissed.
Robertson petitioned the court on the basis of a law change in 2006 in Virginia concerning trusts, but the law changes were not in effect when Robertson signed the credit agreement in 1998, the newspaper said.
The trust sold CENCO to EMC Capital Corp. in 2004.