President Reagan's inaugural committee, which ran the costliest inauguration in American history, will now have to make the most refunds ever -- at least $450,000 to persons who never received tickets or were turned away from expensive inaugural festivities that had been oversold.

The total amount of refunds could exceed the $450,000 mark if the committee's legal department decides, for example, that ticket-buyers who gave up after waiting in line for 30 minutes deserve a refund. The criteria for refunds still is being discussed, officials said.

"We simply underestimated the demand for tickets," inaugural cochairman Robert Gray said when asked about the record number of refunds, compared to $60,000 refunded by Jimmy Carter's inaugural committee. The refunds will not prevent the committee from paying its bills and netting a "good profit," Gray said.

While "unexpected" demands for tickets may have contributed to the refunds, confidential committee memos and interviews with several top inaugural officials suggest that poor management, politics and, finally, panic also played a major role in what some officials are calling the "ticket fiasco of 1981."

Reagan's committee had planned to make its invitation and ticket dispersing process a standard-setter for years to come.

Reality proved far different from the dream. Some ticket-buyers had to wait three hours and when many of them reached the front of the line, they were told the big events were sold out.

Even dignitaries had troubles. Tickets for White House counsel Edwin Meese were lost. So were tickets for dozens of congressmen.

The groundwork for the ticket disaster actually began in December, Gray says, when various state Republican officials missed their deadline for giving the committee names of persons who needed invitations. By Dec. 21, the entire invitation procedure was a week behind.

Desperately, the committee set up several telephone banks and sent out word that guests could call in their inaugural orders and charge the cost on credit cards.

"When they sent out invitations in the mail, it specified how many tickets you were invited to buy," an official explained, "but we had regular salesmen on the telephone banks. When someone called to buy a ball ticket, the salesman would ask how many they wanted and then mark them down for that many."

A few days after the telephone banks started, bags of mail began arriving with ticket orders. By Jan. 11, after the telephone lines were shut down, at least 1,500 tickets and possibly as many as 3,000 tickets had been oversold, according to inaugural officials. Some of those tickets had been sold to VIPs who had paid up to $1,200 for a box at the Kennedy Center ball.

According to Gray, about 1,000 checks sent to buy tickets to a gala held at the Capital Centre after it was sold out will be refunded.

About 200 people were turned away from the inaugural ball at the Sheraton Washington, Gray said. He does not know how many ticketholders went to the Kennedy Center ball and were turned away by fire marshals who refused to let anyone in for one 30-minute period because a crowd estimated at 12,000 had swarmed into the 8,000-capacity hall.

Gray said an unknown number of ticket-holders also were turned away from the youth hall at the Mayflower Hotel.