Is it a crime to commit a crime that has been commissioned by the FBI? That's just one of the questions proliferating in the case of Jackie Presser, Teamsters president, Reagan loyalist and, it is alleged, a spy for the Federal Bureau of Investigation.

Presser, the only big-time labor leader to support President Reagan, denies he moonlighted for the G-men, but his uncle, Allen Friedman, fingered him in open court and a federal judge believed him.

In 1980, Presser was under investigation by the Labor Department for suspected "ghosting" -- that is, paying people for no work. Labor sleuths found out that indeed ghosts were walking the Teamsters payroll. What they didn't know was that Presser was engaged in the indictable practice under orders from the FBI.

After a 32-month investigation, the Justice Department decided not to indict Presser, even though a Cleveland strike force strongly recommended it.

Two men were indicted for their part in Presser's government-sponsored criminal activity. Friedman was let out of jail this week and granted a new trial by federal Judge Sam H. Bell. Now John Nardi Jr. is clamoring for exoneration. He was awaiting his sentence, the length of which was to be determined by the measure of cooperation he gave in testifying against Presser.

The two made the quite reasonable claim that important evidence had been withheld from their lawyers. If Presser were an FBI informer and engineered the crime, they might successfully plead entrapment.

Why was Presser working for the feds? He was an effective, modern labor leader, who used high technology and state-of-the-art public relations to change the image of his union as corrupt and mob-ridden. He certainly didn't need the money. His Teamsters salary is $225,000, and he had a spectacularly successful sideline in a theater-night club in Cleveland and other real estate investments.

Was the case a simple matter of the right hand of government not knowing what the left hand was doing? But in strike-force actions, all agencies are involved and share information.

Why did the FBI stand by and let the cases against Friedman and Nardi go forward when it knew that the verdicts would be overturned if Presser's services to the FBI were revealed?

Why didn't the FBI tell the Justice Department that Presser was their pigeon? Why didn't the FBI, usually a model of bureaucratic correctness, even tell the FBI? The bureau's director reportedly didn't know anything about it. Why was a federal grand jury kept in the dark about Presser's other life as an informer?

To allow the case to proceed without that critical information could constitute fraud against a grand jury.

Presser isn't talking. Neither is Attorney General Edwin Meese III. His story is that he "recused" himself from the case because of his desire to free the matter from any taint of political influence -- he was in the White House while Presser was being wooed and was extremely proud of the endorsement. Since he took office six months ago, Meese has been exceptionally vocal on all manner of subjects. But he is mum on the question of Jackie Presser. So are his deputies.

"Nobody's tried to cover this up," Meese declares defensively.

Two Senate committees are investigating. The FBI has begun a belated inquiry into its own conduct, and the Justice Department has called in its Office of Professional Responsibility to try to find out what in the world was going on.

But it is a federal judge who is, once again, offering the best hope of solving a smelly mystery. Bell, in ordering a new trial for Presser's uncle, said, "I think it's time we all dispel the shadow of rumor and innuendo and shine the light of truth on the happenings before the last trial."

Maybe we will even hear why the FBI sent a shark after some minnows. Usually, little fish are used to bring in the big ones. But they started at the top with Presser -- and then made sure he committed the crime they suspected him of.

Whatever the outcome, Presser is, in the eyes of one fellow union leader, a loser. Says William W. Winpisinger, president of the International Association of Machinists: "He'll have to go to work in a bullet-proof limousine. I don't know anyone who respects a stool pigeon either in or out of the trade union movement."

The Reagan administration, which talks big about moving against crime, will have to do something fairly soon unless it wishes people to reach the obvious conclusion about the affair, which is that Jackie Presser walked because someone in the Reagan White House was watching over him.