The nation's top 100 electric utility companies overcharged their customers by $3.7 billion in 1981 because of a federal law that requires utilities to incorporate into their rates taxes that are never paid, an environmental group said yesterday.

According to a report by the Environmental Action Foundation, the utilities billed ratepayers for $5 billion in federal income taxes but paid only $1.3 billion to the federal government that year. Of the 100, 17 paid no taxes at all in 1981 but billed their customers for taxes for that year nonetheless, the foundation reported.

The study said that the overcharge results from a federal law adopted in 1969 that requires utilities to keep two sets of books. One set is used for determining rates and the other for tax purposes, the EAF said. The law also prevents state utility regulators from blocking tax overcharges, according to the group.

The non-profit environmental advocacy group called on Congress to chance that law and others that provide tax breaks to utilities.

According to the study, Potomac Electric Power Co. charged customers for $67.2 million in taxes in 1981 but paid $19.56 million, resulting in an overcharge of $47.64 million. Virginia Electric & Power Co. charged customers for $93.67 million but paid $22.75 million, resulting in an overcharge of $70.92 million. Baltimore Gas & Electric Co. charged ratepayers for $86.7 million in taxes in 1981 but paid $57.28 million, resulting in an overcharge of $29.42 million, according to the report. Representatives of the three utilities could not be reached for comment last night.

The report charged that the average utility customer paid more than $50 in 1981 in what the report called "phantom taxes." The phantom taxes result from measures that reduce or postpone tax liability for a utility when it makes a new investment. The figures in the report were based on a survey of recent annual reports filed with the Federal Energy Regulatory Commission, the group said.

Economist Richard E. Morgan, who directed the study, said that utilities claim that the deferred taxes and tax credits eventually are paid to the government or returned to consumers. In the meantime the utilities say the money is invested in new power plants.

Morgan disputed the utilities' claim and said that unpublished figures prepared by the U.S. Department of Energy put the industry-wide total for deferred taxes at more than $25 billion.