The day he began his career as a professional investigator in 1934. Carmine Bellino was told by a fellow FBI agent to leave his accounting books behind and bring his gun - John Dillinger and Baby Face Nelson were on the loose after killing one G-man and wounding another.

That was not, as it turned out, the way Bellino's career went from that day forward. He had his share of the spotlight and colorful cases, but his weapon of choice over the next 40 years or so was the ledger sheet and not a gat.

In a career that took him from the right hand of J. Edgar Hoover to the inner circle of Robert F. Kennedy, Bellino worked methodically with figures - Hepling to send Teamster president Jimmy Hoffa to jail and tracing the complicated money chain of the Watergate cover-up.

Yesterday Bellino, now 73 and as retired from work as private clients will let him remain, stood in front of 30 government investigators a generation or two his junior and told them how to go about catchiing white-collar criminals.

Much of what he had to tell them in the seminar at Columbia, Md., involved the tedious and time-consuming process of checking numbers, sifting through records, reading between lines in the quest for clues. The idea, Bellino told them is to make the figures talk. Rather than suggesting shorts cuts, Bellino set a theme of thoroughness. "Develop your leads, don't just close them," he told his audience at one point.

Bellino illustrated his principles with examples drawn from experience. He illustrated circumstantial evidence with what he called the "House of Pleasure" case. While investigating a situation involving illicit sex in Atlantic City, Bellino said he was advised by another agent to determine from a local laundry the total number of towels delivered weekly to the house and divide by two, multiply by the "going rate" and he would have the establishment's gross weekly income.

Bellino, renowned for his insistence that he see all available documents, told of another case where a public official in Alaska sent radio messages - later confirmed in writing - in which he proposed illegal deals and mentioned bribery. In each instance, the official directed that the message be destroyed. But, Bellino said the official's own file - when obtained - had maintained intact his own copies of the messages.

The lecture also included a tip on how to pick up traces of hidden bank accounts - look for regular personal expenses, like an insurance policy, paid by check and if the subject misses a payment find out from the insurance company if he paid and, if so, how. If by check from another account, you may have discovered a clandestine account.

Another way to find hidden bank accounts that was available to him but now is denied government investigators. Bellino suggested, is the use of "mail covers" - opening the mail of investigative subjects. "No," several of the investigators assured Bellino, "we still use those."

Bellino's appearance was part of two-week seminar being conducted for investigators from the Offices of Inspector General for the departments of Housing and Urban Development; Health, Education and Welfare, and Agriculture. President Carter, who last May urged that more attention be paid to white collar crime, signed into law in October the INspector General Act of 1978-creating offices in 12 major U.S. agencies to investigate fraud and abuse and report directly to the attorney general.