Mayor Walter E. Washington has signed legislation to allow legitimate theaters to serve liquor during intermissions and to lower the District of Columbia's tax on liquor by 10 cents a fifth, his office announced yesterday.

The measure will become law unless disapproved by Congress. The congressional review procedure will take at least two months.

Under existing law, only the John F. Kennedy Center for the Performing Arts, which is on U.S. property, is permitted to serve liquor. The new measure would extent that right to other theaters, including Arena Stage and the National Theater. The National's management has indicated it will not take advantage of the liberalized law.

The main announced purpose of the legislation is to provide more than $3 million a year in added revenue for the theaters. That is based on an estimate that more than 2 million drinks will be sold at $1.50 each.

The liquor tax reduction was proposed by Council member Marion Barry (D-large) and is intended to make Washington liquor stores more competitive in price with those in the suburbs. In recent years, prices in D.C. stores have risen higher than those in most suburban areas.

Under the measure's provisions, the present tax of $2 a gallon will be reduced to $1.50.