Auto sales dipped sharply in the first 10 days of April, as the end of industry's cash rebate programs hit General Motors Corp. particularly hard.

Sales of American-built cars were 11.8 percent below the depressed level of a year ago, with GM's total down nearly 23 percent.

Ford Motor Co. and Chrysler Co., both hurt by an effective GM sales campaign a year ago, gained ground against the top American manufacturer in the beginning of April. Ford's sales were up 4.8 percent over last year while Chrysler reported a 32.9 percent increase.

Chrysler's continued improvement enabled the company to take a "who needs you?" attitude toward Ford, following Ford's rejection last week of a Chrysler query about a possible merger or joint manufacturing venture between the troubled No. 2 and No. 3 American automakers.

Chrysler Chairman Lee A. Iacocca said, "We have read the press statement from Ford expressing their lack of interest in holding discussions with Chrysler. We accept that decision. We have not pursued it further and we have no plans to do so.

"Discussions are continuing with several companies, which see the potential of a long-range relationship," Iacocca said, without naming them. Chrysler had sent a proposal to Ford outlining a possible combination of product lines, but company officials said Ford Was never the first choice.

The rebound in sales is permitting Chrysler to be more choosy in negotiating potential joint ventures, a company official said.

A sales slump was anticipated following the end of the rebate programs last month. Companies had reduced sticker prices by $500 to $700 per car to pull customers into showrooms, but the sales gains in February and March came at the expense of business later on. GM suffered most because its rebate was generally limited to cars in stock, while Ford and Chrysler also paid rebates on cars ordered for future delivery, some of which showed up in the April figures.

GM reported sales of 94,023 cars in the April 1-10 period this year, down 22.9 percent from 121,921.

Ford U.S. sales totaled 40,621, up 4.8 percent from 38,755 a year ago. Chrysler listed sales of 20,444, or 32.9 percent above the 15,384 figure of last year.

Volkswagen of America had domestic sales of 3,913 down 9.6 percent from last year's 4,328. American Motors Corp. sales were estimated at 4,300, down 10.6 percent from the 1980 figure.

In the Feb. 11-20 period, during the peak of the rebate campaign, GM sold 99,853 cars, Ford sold 40,368, and Chrysler 19,294. Volkswagen's sales were 5,472 and AMC's estimated sales were 2,500.