Ground has been broken for the American Society for Personnel Administration's new $3.1 million headquarters office building in Alexandria. The four-story Georgian brick colonial building will be located at 606 N. Washington St.

The building's design incorporates an existing late 19th century two-story townhouse on the site. The Alexandria Board of Architectural Review suggested the townhouse be maintained because of its historical significance.

The new building will contain 26,000 square feet of office space and two levels of underground parking. The society will initially occupy about 13,000 square feet on two floors, along with some storage space. The remainder of the building will be leased.

Financing for the construction was secured through an industrial revenue bond approved last October by the Alexandria City Council. First and Merchants National Bank of Richmond is financing the bond.

The society is relocating its headquarters from Berea, Ohio. Completion is expected for late 1983.

Other recent developments in commercial leasing in the Washington metropolitan area:

* The former Postal Service Training Academy, 7900 Wisconsin Ave. in Bethesda, has been remodeled at a cost of about $1 million after the Postal Service's move to a new location in Potomac. Loewinger and Birks Real Estate Partnership of Bethesda has relocated and leased 1,700 square feet of space in the building and Derenberger Reporting Co. of Bethesda has also relocated and leased 955 square feet of space. The Tandy Corp. has leased 2,400 square feet on the ground floor for a new Radio Shack Computer Center which has opened. The Holiday Health Spa on the ground floor has leased an additional 3,000 square feet of space.