The Federal Aviation Administration yesterday grounded another commuter airline, Iowa-based American Central, because of more than 20 safety violations, including falsified pilot records and dangerously overweight airplanes.

In another development, Transportation Secretary Elizabeth Hanford Dole ordered her ethics office to check into contacts that former FAA deputy administrator Michael J. Fenello has had with FAA employes since Fenello became operations director at Provincetown-Boston Airlines (PBA), also a commuter airline.

Depending on the outcome of the review, a formal investigation could be ordered or the matter could be dismissed, a senior department official said.

PBA was grounded by the FAA Nov. 10 for many violations of safety regulations, but was permitted to resume partial service on Nov. 25, after FAA inspectors rechecked its pilots, records and equipment, and after Fenello had joined the airline.

On Thursday, a PBA flight crashed on takeoff from Jacksonville International Airport, killing all 13 on board. National Transportation Safety Board specialists were attempting yesterday to determine why the vital tail section fell off the Brazilian-made Embraer 110 almost immediately after it left the runway.

"It's really a puzzle," said safety board vice chairman Patricia Goldman. "We're not sure what came apart first."

Later in the day, PBA voluntarily grounded its fleet of Embraer 110s, which also are used by other commuter airlines. Federal officials said they were closely watching the Jacksonville investigation, but had no basis for grounding the 110s nationwide. There are 130 of them in the United States and 450 worldwide.

Embraer has offered airlines an optional modification to the tail assembly, aviation sources said, but the modification was neither made nor required on the crashed plane. New model 110s include the modification, the sources said.

Earlier this week, another major commuter carrier, Atlantic Southeast, voluntarily suspended operations briefly after three of its aircraft suffered in-flight engine shutdowns on the same day, a knowledgeable source said. An easily correctable engine icing problem was discovered to be the cause and the airline resumed service, the source said.

So far this year, at least 36 people have been killed in commuter airplane crashes. Thirteen were killed last year. Major airlines have not had a fatal crash in more than two years.

The commuter air business is growing by leaps and bounds, replacing major airlines in providing generally short-hop service between small communities and airline hubs such as Chicago.

Because of that growth, and because the commuter safety record always has trailed that of the major carriers, there has been concern on Capitol Hill that the FAA is not adequately staffed to maintain surveillance of these small airlines.

The Reagan administration cut the FAA's inspector work force from 638 to 534 in 1981, but congressional reaction forced restoration of those cuts. There have been no increases, however, despite the proliferation of airlines.

Dole, on "Meet the Press" last December, announced a "white gloves" inspection of the nation's airlines to underline her often-stated emphasis on transportation safety. Every airline, big and small, was supposed to have been checked.

Dole has yet to release the report on those inspections.

American Central, the airline grounded yesterday, serves 23 cities in eight midwestern states. It was fined $18,000 in civil penalities for safety violations earlier this year, FAA spokesman Dennis Feldman said. "Because of continued flagrant violations, the emergency revocation" of American Central's right to fly came yesterday, he said.

Unlike the PBA suspension, where inspectors worked long hours to restore partial service within 15 days, there are no plans "at this point" to help American Central back in the air, Feldman said.

Terry Hudick, American Central's president, was unavailable.

Feldman said the American Central violations fell into three categories: falsification of flight-crew training records, violation of federal flight-time maximums and violation of weight limits.

He said that pilots were permitted to fly longer between rechecks than regulations permit; that one flight crew had flown for 16 straight hours without rest, in violation of standards, and that one pilot permitted a passenger to board a flight although the plane already was at its maximum allowed weight and the pilot knew it.

Alan R. Stephen, operations director for the Regional Airline Association, which represents many commuter airlines, said yesterday that commuter airlines will carry about 27 million passengers this year, up from 11 million in 1978, when the airline industry was deregulated and major carriers abandoned many small cities.

About 160 commuter airlines now provide service to 600 communites in the contiguous 48 states.

"There are a lot of airline executives in our industry who view these episodes as damning to the public trust," Stephen said. "Perhaps one or two of the airlines out there are not playing by the rules. It is the FAA's job to enforce its regulations . . . . We need that kind of assistance and questioning" from FAA inspectors, he said.

The ethics inquiry into Fenello's contacts was ordered by Dole after The Washington Post reported that some FAA employes had talked with Fenello. All contacts, those employes said, came after PBA had restored partial service, although PBA still is seeking full restoration of its operations.

It is a violation of the Ethics in Government Act for a former senior federal employe, as Fenello is, to represent anyone in an attempt to influence his former agency. Fenello has not returned several phone calls from The Post