The number of new residential units authorized for construction in the Washington area in 1981 dropped to the second-lowest level since 1970, a new report by the Metropolitan Washington Council of Governments showed.

The 1981 figure of 14,078 units authorized for construction represented a 28 percent decline from the 19,710 in 1980.

Other details of the COG report show that:

* Arlington, Loudoun and Prince George's Counties were the exceptions, experiencing an increase in building permit activity between 1980 and 1981, while all other local jurisdictions had decreases.

* A trend continued toward increased construction of single-family housing, with 81 percent of those units authorized in 1981 coming under that category.

* Permits were down for both single-family and for multi-family units, but the decline in the multi-family category was greater. Single-family permits issue in 1981 declined to 11,466, a 24.6 percent drop from 1980. At the same time, permits for multi-family construction dropped 41.9 percent from 1980 levels to 2,612 in 1981. That was the lowest level of activity for that sector since 1975.

* A majority of the multi-family units will be sold as condominiums.

* No permits have been issued in the past two years for rental apartment construction without federal assistance.

* There has been a trend since 1970 toward construction of a greater percentage of housing to be sold than housing to be rented.

Copies of the COG report, Summary of 1981 Residential Building Permit Authorizations for the Washington Metropolitan Area, are available for $7 from COG's Metropolitan Information Center, Suite 200, 1875 Eye St. NW.