A policyholder's complaint has triggered a public hearing that could roll back the 4.2 percent increase in premium rates recently announced by Government Employees Insurance Co., the District's largest insurer of automobiles.

James R. Montgomery III, acting superintendent of the D.C. Insurance Department, scheduled a hearing for Jan. 11 after a protest against the premium increase was filed by the lawyers for the policyholder, who was not identified.

Ron M. Landsman and Peter K. Matt, the lawyers, contended in the protest that Geico's rates do not reflect income the insurance company earns from investing money that policyholders pay in premiums, as required by D.C. law.

"We continue to believe that Geico's data filed with the insurance department shows the need for a substantial rate decrease, on the order of 10 percent," their letter declared.

Montgomery, in ordering the hearing, said in a notification to Geico that his investigation showed "grounds to believe that Geico's new rates are not in accordance" with the law as it relates to investment income, and that "there is a necessity for an adjustment in the rates." The hearing will begin at 10 a.m. Jan. 11 in his office, 614 H St. NW, Room 512.

Geico, which insures about one of every five insured cars in the city, put the new rates into effect Dec. 21, subject to possible rollback. The first premium increase for District car owners in two years, it would raise the average annual premium from about $436 to about $450.