The Arlington County Board, which has heard numerous complaints about taxi service at National Airport, voted last night to ask the Federal Aviation Administration, the airport's operator, to consider regulating taxis there or to permit Arlington to do it exclusively.

The FAA, which now leaves taxi regulation to the local jurisdictions, has proposed new rules to limit the number of cabs that crowd the bustling airport and wants to tighten control of the cab drivers by a special permit system.

Under the FAA's proposal, drivers would hold permits, perhaps costing $100 annually, that could be revoked for violating airport traffic laws or for drawing proved complaints from passengers.

FAA officials have said their proposals are in response to repeated complaints from passengers about the difficulty of getting a taxi and the rudeness of drivers who sometimes overcharge, don't know their way around the area or force them to double up.

County Manager Larry J. Brown complained last night that the FAA's proposals don't go far enough. "The solution is in regulating, not taxing, taxis," he said.

The county staff proposed that the FAA become the licensing jurisdiction for airport cabs and establish rules that would restrict the number of cabs and require them to use meters. Board Vice Chairman John G. Milliken suggested asking the FAA to allow Arlington to become the licensing authority.

Arlington officials are particularly concerned because National Airport is located in the county. "As such it conveys to some air passengers that Arlington is responsible or involved in the quality of service," Board Chairman Ellen M. Bozman wrote to the FAA in a letter the board authorized last night. The letter also notes that the board is "concerned because many of the air travelers stay in our hotels and/or do business in Arlington."

The board's action came in response to the FAA's request for reaction to its proposed permit program from local governments.

In other action last night, the board:

Asked the FAA to delay implementing a proposed reduction from the required four-person carpools to two-person carpools on the Dulles Airport Access Road connector to I-66, scheduled to open this fall. The board said the plan should be delayed until the FAA devises a failsafe reliable way of preventing commuters using the Dulles access road from continuing onto I-66 during rush hours.

Reconsidered its Monday night 4-to-1 vote on development around the Virginia Square Metro stop to allow board member Walter L. Frankland Jr., who voted against the plan, to change his vote. During the reconsideration, board member Dorothy T. Grotos, who voted for the plan Monday, changed her vote. Grotos wanted the board to establish a clear priority for a supermarket in the area instead of listing it with other goals. the board has for the area. The board reaffirmed its pledge to use "all legal tools available" to assure the inclusion of a supermarket in any future development, as residents of the area have urged.