By the time Chris Christie became governor of New Jersey, the state’s auditors and lawyers had been battling for several years to collect long-overdue taxes owed by the casinos founded by his friend Donald J. Trump.

The total, with interest, had grown to almost $30 million. The state had doggedly pursued the matter through two of the casinos’ bankruptcy cases and even accused the company led by Mr. Trump of filing false reports with state casino regulators about the amount of taxes it had paid.

But the year after Governor Christie, a Republican, took office, the tone of the litigation shifted. The state entertained settlement offers. And in December 2011, after six years in court, the state agreed to accept just $5 million, roughly 17 cents on the dollar of what auditors said the casinos owed.

Tax authorities sometimes settle for lesser amounts to avoid the costs and risks of further litigation, legal experts said, but the steep discount granted to the Trump casinos and the relationship between the two men raise inevitable questions about special treatment.