As a federal grand jury this week began examining allegations of official indifference to Alexandria's once-flourishing bingo and massage parlor operations, William H. Cowhig, Alexandria's chief prosecutor, was making his usual afternoon rounds - on the Belle Haven Country Club golf course.

To Cowhig, who has become a subject of the grand jury's inquiry, golf is an avocation he pursues often, whether under investigation or not.

But to his critics, Cowhig's golfing is symtomatic. If Cowhig had spent more time pursuing allegations of corruption in the city, the critics say the federal grand jury probably would not have been convened.

After 25 years as public and private lawyer in Alexandria, Billy Cowhig has remained as firm in his statements of his innocence as he has been in his view of this office. It is his view of the office of commonwealth's attorney for the city - as much as some fo the recent allegations - that have made the ruddy-faced, balding lawyer a focus of the federal probe.

In sharp contrast to other Washington area prosecutors, Cowhig contends that his is strictly a prosecutorial office. He will press any criminal charges that other officials, including the police, file. But he will not initiate criminal investigations on his own or file charges on his own.

"My office is not an investigative one, it is a prosecutorial office," he said. That view has brought him into conflict with the Alexandria city manager, the city's police chief and others who wanted stronger action and leadership from Cowhig in the investigation of bingo and massage parlor operations.

"The commonwealth's attorneys have all the authority and power they need to be strong in their areas," said one knowledgeable state crime expert in Richmond. "You've got to interpret the law to suit your feelings. Some of them are good attorneys with real smell for the criminal process. Cowhig is slow in this area."

At the same time, many of the recent disclosures about the 52-year-old prosecutor provide glimpses of a man who as a private pilot was flying off to vacations at a resort hotel he and others own on a remote Caribbean island.

Two of the men involved in bingo investigation were former Cowhig law clients, one of whom vacationed with Cowhig at the Two Turtles Club he owns with others one the island of Exuma, 300 miles south of Miami.

The Two Turtles Club and Cowhig's involvement in it has surfaced as a key element in the federal investigation. Cowhig has said he purchased it with three relatives 10 years ago for $215,000 and that it has been a financial failure. He tried several years ago, to the dismay of some, to enlist local lawyers and others as financial backers in the project.

He has, according to his own account, failed to meet the monthly $1,800 mortgage payments on the hotel for several years. First American Bank of Virginia, which lent him and his relatives $150,000 for the hotel's purchase, has allowed him to maintain the loan by making interest-only payments, he said.

The hotel's mortgage could have been a major financial drain on Cowhig's $42,500-a-year prosecutor's salary, and he concedes that his arrangement with the bank is unusual. "It is an arrangement based on my reputation of 25 years of honesty in this city," he said the other day.

A Customs Service official has said part of the grand jury probe is dealing with the question of whether federal currency laws were broken by people shuttling in and out of the country with large, unreported amounts of cash. Under the law it is illegal to carry more than $5,000 in or out of the country without reporting it to the government.

Cowhig said the mortgage, originally scheduled for repayment in 10 years, has been reduced only to $114,000 during that period. He said a lease of the hotel to a resident operator last November now provides enough income for "us to almost break even."

Cowhig's coinvestors are his two stepbrothers and stepsister, the children of the late Alexandria District Court Judge James Colasanto. Cowhig said the financial worth of the families that have invested in the club "is about $1 million."

His ties to the Colasanto family are one measure of his position within a conservative element of Alexandria's Democratic party. He was first elected prosecutor in 1973 after twice losing Democratic primary races. He won in 1973, defeating John Kennahan, his Republican predecessor, and then winning reelection last year without opposition.

Cowhig's style is often contrasted with Fairfax County prosecutor Robert H. Horan. "Horan let everyone know he's the top law enforcement guy there, he lays down the law to the police and everyone," said a state law enforcement official yesterday, "Cowhig does not."

However, his style wins Cowhig points with some lawyers.

"It is important to keep in mind that it is not Cowhig's responsibility to get warrants and make arrests," Alexandria Bar Association President Roger L. Amole Jr. said in an interview.

"The commonwealth's attorney has a major law enforcement policy role to play," Amole said, "and in that area I give Cowhig high marks. He has taken a stand for vigorous punishment of criminal offenses and has called on the courts to carry it through. I think he has been effective."

Amole also praised Cowhig for his work as the chairman of a bar association committee that recommended ways to speed the court process in Alexandria. The proposals were adopted by city judges last year.

In April, Cowhig removed himself from prosecution of bingo violations when the vigor of his enforcement of the laws was questioned and after disclosure that he had operated a game for three days for an Explorer Scout group he helped form.

It was later disclosed that one of Cowhig's former clients operated a bingo game without a permit and another has leased space to a bingo operation that has been the focus of a police investigation.

When city official wrote Cowhig that former client James Fike had operated a game without a permit, Cowhig wrote back that Fike had promised him he would not do it again. Cowhig told the official, finance director Howard J. Holton, that he would prosecute Fike if Holton brought charges against Fike.

In the case of the second former client, Edward L. Hinkle, city officials deliberately kept secret from Cowhig their probe of a bingo operation in a building leased from Hinkle. That investigation has produced no charges.