It's hard to imagine a situation in which some people send bum checks to the government and get silver dollars in return while others send in valid checks and end up with no coins.

Yet, such a mixup acutally occurred last spring when the General Sevices Administration (GSA) held a sale of its remaining stock of antique Carson City silver dollars. Hundreds of Americans were disappointed or incensed enough to complain to Rep. Frank Annunzio (D-Ill.), who had introduced the bill authoizing the sale.

Yesterday Annunzio held a hearing to determine what went wrong. The General Accounting Office, which had been called in to invesigate GSA, painted a picture of bureaucratic bungling. But GSA protrayed the Carson City sales as yet another casualty of the great silver debacle, courtesy of the Hunt brothers of Texas.

When the sale was announced, silver was selling for $16 an ounce; public response was tepid. After all, there had been five previous offerings of the Carson City sivler dollars which were minted before the turn of the century. But on Jan. 21 the price of the precious metal skyrocketed to $50 an ounce. Just over two weeks later the GSA put the coins -- 90 percent silver -- on sale at between $45 and $65 each.

Speculators as well as numismatists overwhelmed the part-time staff GSA assigned to the project. GSA had expected to receive 200,000 orders over a two-month period. It got nearly double that number in the first 10 days alone -- 500,000 all told. Americans sent in over $300 million in checks to buy less than 1 million coins.

Rather than send each person one or two coins until they ran out, GSA elected to fill 200,000 orders at random.

Consequently, some people got up to 35 coins; 300,000 others got nothing. Roy Markson, GSA Commissioner of federal property resources service, testified that parceling them out equally would have doubled administrative cost.

As of July 28, 3,795 of the 500,000 checks received had bounced, GAO found. The government was stuck with $8.1 million in bum checks but by canceling orders managed to cut its loss to 714 checks with a face value of $1.1 million. (By Aug. 18 the debt had been whittled to $312,922 after GSA wrote the delinquent customers asking them to make the checks good.)

Coins or refunds were issued to these 714 persons, even though GSA's cashier had been notified by the Federal Reserve Bank that many of them has bounced.

Moreover, GSA cashed more checks than they had coins to sell to cover bad checks. Markon was at a loss to explain why some persons who sent in valid checks six months ago still have not received refunds. Observing that some of the checks amounted to several thousand dollars each, Annunzio said constituents had complained about making "interest-free loans" to the government. The Treasury, incidentally, made a $40 million profit on the sale.

GSA also is handling the current sale of gold medalions. Fortunately for the agency,there has been no gold rush. The medallions' prices are set at market value daily. With the campaign almost half over, it has received orders for just 275,732 out of the 1.5 million medallions it has for sale. But the GSA is taking no chances. It will accept no personal checks, and the delivery time has been increased to between eight and 12 weeks.