NEW HAVEN — The $44,000 question was whether the city’s Board of Police Commissioners has the authority to fire an allegedly corrupt cop even if the officer beats it to the punch by putting in for retirement first.

The answer is “no,” and now the city must pay a former police lieutenant tens of thousands of dollars in retirement benefits it improperly denied after his arrest on federal corruption charges.

In a decision dated Feb. 15 and received by the city Thursday, a labor arbitrator ruled that, under the union contract, former Lt. William White was in effect already retired when the Board of Police Commissioners fired him April 4, 2007. As such, he is entitled to a lump sum payout for accumulated sick time, unused vacation days and holiday pay, which the city had refused to give him. That means White, 64, who is scheduled to be sentenced to a likely federal prison term in April, will get about $44,700 from the city as well as a roughly $3,000 bump in his annual $91,000 pension, an attorney for the police union said.

Mayor John DeStefano Jr., in a statement, called the language in the contract “unfortunate.”

“When someone fails to uphold their oath to the community, breaks their trust and behaves in the manner that White, (and former detectives Justen) Kasperzyk, (Jose) Silva and (Clarence) Willoughby did, they don’t deserve to be able to retire from the Police Department nor do they deserve the benefits that accompany that designation.”

Sgt. Louis G. Cavaliere, the union president, however, described the award as “great victory” for all officers, and not just White. He contended the city took a position it knew violated the contract because officials found it politically distasteful to pay White benefits to which he was entitled.

“All this fight was about was our contract language, not about Billy, Justen, Jose or anyone else in this department. If they were allowed to get away with this, then they could arbitrarily take away any benefit in this contract because they don’t like a person.”

The city held that the police board had the sole authority to hire and fire, but now that’s not necessarily the case when the officer has enough time on the job to retire — and does so in time.

The arbitrator’s decision had broader implications that already affected how the city deals with officers who find themselves in the cross hairs of internal probes.

Indeed, hours after the decision was announced, the city canceled a disciplinary hearing for Willoughby, who was arrested Feb. 6 for allegedly stealing from the department’s confidential informants fund and put in retirement papers the same day. He was scheduled to appear before the Board of Police Commissioners Thursday night, but the city told the union it planned to drop all departmental charges against the 24-year veteran. The pending criminal case will continue.

“The arbitrator’s ruling made making a decision on whether or not to terminate Willoughby a moot point,” said Richard Epstein, chairman of the Board of Police Commissioners.

White, former head of the department’s narcotics squad, was arrested March 13 as part of a federal corruption probe into theft and bribery. He was accused, and later pleaded guilty, to taking bribes from bail bondsmen and stealing tens of thousands of dollars planted by the FBI, including $27,500 hidden in the trunk of a rented car that was wired for audio and video. He took the cash despite expressing concerns it might get an informant killed and wrote “estupido” on the empty bag to throw off fictitious drug dealers. Kasperzyk and Silva, two of his detectives, were arrested and pleaded guilty as part of the same probe.

The police union had filed a grievance on White’s behalf last year, arguing the 39-year veteran was retired as of March 15, 2007, the day he filed his pension application.

The police board fired him on April 4 and the city argued it had authority to do so because the Police and Fire Pension Board had not yet voted on his pension. The pension, which was an entitlement under the union contract, was approved on April 12 retroactive to the day he put in his papers.

The city argued the pension board’s function is to administer provisions of the pension plan, and it is the police board that determines whether a person is retired or terminated.

The arbitrator agreed with the union, concluding jurisdiction over pension applications is with the Police and Fire Pension Fund and not with the police board.

The city is looking to negotiate with the union to include a “bad boy clause” in the next contract to “divest” employees of pensions and related benefits if they are found guilty of using their position to violate the public trust.

Cavaliere said the union is willing to listen.

“It’s a give and take,” he said.