Police here have uncovered a confidence game in which thousands of airline tickets are being obtained at no charge, but airlines have declined to file complaints because of fear that publicity would show the general public how the simple con works.

Police in Providence and nearby Warwick, R.I., have hard evidence -- thousands of dollars worth of airline tickets mailed to con men using phoney names, Providence's Evening Bulletin reported in today's editions. But the airlines involved, Braniff, Delta, American and Eastern, have declined to press charges despite repeated police requests.

According to police, the con game is a sideline for several men involved in a national counterfeiting ring. The men have used the illegally obtained tickets to crisscross the country free, have sold some of them at one-third of their normal price and have turned some of them in to airlines for cash rebates, sources siad.

Although authorities are uncertain how much money is involved or whether other airlines have been victimized, one airline reportedly sent $2,000 worth of tickets to the con men on a single day last month. Sources said the men have been employing the confidence game for years.

The con works this way:

The con man, giving a phoney name and a temporary address, calls an airline and makes reservations for several persons on a flight. The airline sends the tickets in the mail with the understanding that they will be paid for within 72 hours by return mail. The tickets are marked with the code "TBM," indicating that they are not good until paid for.

When the con man receives the tickets, he brings them to a second airline, explaining that the first airline's flight is inconvenient for him. The second airline exchanges the tickets marked "TBM" for tickets that are considered paid for in full.

When the second airline submits the original tickets to the first airline for reimbursement, the first airline discovers it cannot collect from the customer.

The airlines declined to talk about the situation.

William Osmond, spokesman for the Air Transport Association, a group representing most U.S. airlines, acknowledged in Washington that the industry is aware of the practice. He offered no additional comment.