The state Department of Motor Vehicles, taking a cue from Gov. Arnold Schwarzenegger, showed its tight turning radius this week by announcing that owners could immediately register their vehicles at the recently slashed car tax rate.

The owners of an estimated 5 million cars and trucks in California who have received registration notices at the formerly higher rate have been invited to do the math themselves and keep the difference.

Without the change, the department’s antiquated computer system would have required owners to wait until Dec. 19 to benefit from the GOP governor’s action Monday rescinding the tripling of the vehicle license fee. “We think that is a major breakthrough that will please a lot of people,” DMV spokesman Bill Branch said. “I have never seen things move this quickly.”

Less certain is how owners who paid the higher rate after the fee was increased Oct. 1 will receive a refund.

The DMV Web site tells customers who have paid the full amount that they will “automatically receive a refund by mail beginning in early 2004.” But Senate President Pro Tem John Burton said there isn’t money for refunds.

“We’d have to appropriate about $3 billion we don’t have,” Burton said Wednesday. “It can’t go out until someone tells us where the money is coming from.”

The Schwarzenegger administration is counting on the Legislature, which has been called into a special session, to find the money.

“We are saying (the Legislature has) to deal with it,” said H.D. Palmer, a spokesman for the Department of Finance. “There is going to have to be an appropriation.”

For five decades, the vehicle license fee was set at 2 percent of an automobile’s value — until the Legislature in 1998 lowered the amount owners were required to pay.

In June, former Gov. Gray Davis’ Department of Finance pulled a “trigger” restoring the fee to its previous level because of the state’s budget problems. But Schwarzenegger rescinded the increase on his first day in office, as he had pledged during the gubernatorial recall campaign.

The rollback leaves local governments — which use revenues from the vehicle license fee to pay for police, fire protection and other services — with a $4 billion budget hole. Schwarzenegger said the state should “backfill” the money for local governments, but Burton said there is no money to do that.

Meanwhile, the administrative costs of issuing refunds to the roughly 3.1 million car owners who have already paid the higher car tax rate would be $10.3 million, officials said.

Fair Oaks resident Jerry Smith, who recently paid the higher vehicle license fee on his wife’s Chevy Tahoe, said he was glad to hear the state would allow people to immediately pay the lower amount.

The fee this year for the 2000-year model Tahoe was $508, compared with less than $200 last year, he said.

“I know we need the money, but it is not fair to go after one group,” Smith said.

Smith added that he understands why refunds might be delayed.

“It makes sense to me. … You can’t just say, ‘Pay for it,’ and figure out where it comes from later,” he said.

In a related decision, the DMV said car dealers can start selling vehicles at the reduced fee rate and hold on to the payments until the department can reprogram its computers.

Some dealers had blamed a recent slump in sales on the higher fees.