Auto sales for March were still very weak but showed some improvement over February.

Despite these rather awful numbers, the industry said they think things are getting better.

All the big car makers suffered sales declines of 36% or more compared to March 2008. Industrywide, U.S. sales totaled 857,735 cars and light trucks, down 37% from a year earlier, according to AutoData Corp. But that’s up from 688,909 vehicles sold in February and was the highest total since September. February’s sales were down 41% from a year earlier.

The annualized sales pace, a closely watched indicator, came in at 9.86 million vehicles, well below the 16 million or more the industry typically logged a few years ago, but up from February’s pace of 9.12 million.

“I believe we are in a bottoming process for the industry,” Bob Carter, a group vice president at Toyota Motor Corp., said in a conference call. Mr. Carter said the company’s 18% sales improvement in March compared with February could be “a very early indication that we have floored and some optimism is starting to return to the market.”

Michael DiGiovanni, the top sales analyst at General MotorsCorp., said he expects a “very, very gradual pickup” in vehicle sales in the second quarter. He cited “the first signs of brightening” in the market. Jim Press, Chrysler LLC’s vice chairman and president, said, “The market is starting to show small signs of life which need to be nourished like seedlings.” Both GM and Chrysler are seeking additional aid from the government.

It remains to be seen whether the recovery has legs and just how far they take the industry. New financing plans and government purchases of vehicles tied to the fiscal stimulus plan will probably continue to give sales a boost, at least for a few months. The car fleet continues to age as well so a certain amount of replacement buying has to take place.

On the flip side, it’s going to be interesting to see what happens to GM and Chrysler this month. Will consumers buy into a government guarantee of warranties and put their doubts about the viability of the companies aside or will they just say it’s not worth the risk?

Personally, it’s a risk that I wouldn’t want to run. Somehow I just don’t think I would relish trying to get a transmission under warranty serviced under a government guarantee if the dealer who sold me the car had closed up shop.

more: here