The city's gratuitous explanation for settling the controversial Central Park jogger case reveals, yet again, that the words of Mayor Bill de Blasio and his subordinates belie their actions.

How else to describe corporation counsel Zachary Carter's contorted explanation last week for the $41-million settlement to the five black and Hispanic teenagers, known as the Central Park Five, who were wrongly convicted of beating and raping a white female jogger in 1989?

The settlement "should not be construed as an acknowledgment that the convictions . . . were the result of law enforcement misconduct.

"On the contrary," Carter said, "our review of the record suggests that both the investigating detectives and assistant district attorneys involved in the case acted reasonably, given the circumstances with which they were confronted . . ."

So what he's saying is neither the cops nor prosecutors did anything wrong.

"To say there was no official liability is laughable," said Jonathan Moore, the lead attorney for the Central Park Five. "Why else would anyone in his right mind have paid $41 million to settle this case?"

So if nobody did anything wrong, how does de Blasio justify using public money to pay the settlement?

His explanation -- that the city "had a moral obligation to right this injustice, which is why, from day one, I vowed to settle the case" -- explains nothing.

Does Carter's statement mean detectives did not coerce the five teens into implicating each other, as their supporters claimed the police did? Did the teenagers freely implicate each other, perhaps to hide they had beaten up other people at the park, as their detractors have claimed?

Does Carter's statement also mean that lead prosecutor Linda Fairstein did not ignore contrary evidence and properly charged the five with the rape?

Sources say Fairstein, who is now a novelist, put a full-court press on Carter to issue his good-conduct statement, which was immediately echoed by Manhattan District Attorney Cyrus Vance, of whom Fairstein is said to be a major supporter.

There's one way to settle all this: Unseal the entire case record so the public can learn the truth.

As a candidate, de Blasio championed government transparency. Here's his opportunity to show his words don't belie his actions.