Three local Chrysler Corp. auto dealerships have closed their doors this week, leaving customers confused and complaining about the apparently abrupt decisions by the dealers to go out of business.

Bethesda Chrysler-Plymouth, 4924 Hampden Lane, Bethesda, and Capitol Hill Dodge, 90 K St. NE, closed their doors yesterday, following Marlow Heights Chrysler-Plymouth, 3636 Branch Ave., Marlow Heights, which stopped doing business earlier in the week.

There was no public announcement of the closings, which left some customers with their cars in the shop for service and other waiting for new cars to be delivered.

Dozens of sales people, mechanics and janitorial workers were thrown out of work, some with less than a day's notice. An employe of Capitol Hill Dodge said workers there were notified after lunch that the business would close at the end of the day.

A customer who had ordered a car from Capitol Hill Dodge and was waiting for extra equipment to be added before picking it up complained that she was told three different things by three different people when she called about the car.

One person told her, "If you want your car come in tommorrow." An other insisted nothing could be done until Monday. A third said the car - without the extra equipment could be picked up anytime except last night.

"We'll take care of it. Chrysler is going to maintain the warranties," said one Capitol Hill Dodge employe.

Elliot Denniberg, president of Capitol Hill Dodge, promised that all new and used car sales in progress will be completed and all cars in the shop for service will be repaired.

Denniberg said he had been "asked by Chrysler Credit [the company's financing arm] to voluntarily close our store." Another employe of the company said Chrysler had refused to give more credit to the dealership, in effect forcing it out of business. Chrysler will take over the dealership next week and oversee its liquidation, the employe added.

Closing of the three dealerships was the first local fallout from the financial problems of Chrysler Corp., which has asked for $1 billion in federal help to keep the No. 3 auto maker in business.

Yesterday, Chrysler said it had more than 80,000 unsold cars and would ofter discounts of from $325 to $1,000 per car to get rid of them. (See Story Pa ge C-7).

Local auto industry sources said the three dealerships going out of business had to fold before the new 1980 models come out. Chrysler has agreed to repurchase current-model cars from dealers, but after the 1980s come out, dealers will be stuck with any unsold '79s. "Anyone who wants to get out has to do it now or make a commitment for the whole next year," the source said.

At Bethesda Chrysler-Plymouth, vice president and general manager Michael Jackson said the company would continue to operate its parts and service business but would turn the new car showroom into offices and rent them out.

The dealership is owned by a Patrick Douglas, a German count, who also owns Euro Motorcars, a Prince George's County Mercedes-Benz, Porsche and Audi dealership and a Bethesda Mercedes-Benz and Rolls Royce dealership which also carries the Euro Motorcars name.

Jackson said the Chrysler-Plymouth dealership "was not profitable to operate and had not been profitable to operate for quite some time."

No one answered the phone at Marlow Heights Chrysler-Plymouth. Another dealer said the last cars disappeared from its lot on Wednesday.