Perpetual Savings Bank of Alexandria said yesterday that it had purchased a Columbia, Md., auto leasing firm to expand the bank's automobile financing alternatives.

No purchase price was disclosed. The acquisition is the latest in a series of efforts by Perpetual to expand the services it offers customers. Other financial institutions have taken similar steps.

The newly acquired division, American Financial Corp., offers auto leasing programs through about 135 auto dealers in Virginia, the District, Maryland, North Carolina and South Carolina. Perpetual will capture the $100 million in leasing business that American Financial had been spreading among a number of financial institutions, according to Thomas J. Owen, Perpetual's chairman.

Owen estimated that the business could expand to $200 million or $300 million annually within a few years, as changes in the tax law make it more attractive for consumers to lease cars rather than to finance their purchase. Beginning this year, deductions of interest payments on federal tax returns are being phased out, and will disappear completely in 1991.

Because of those changes, Owen said Perpetual wanted to offer customers an alternative to traditional auto financing.

"Our familiarity with leasing in the past has been negligible," he said. Rather than start a leasing operation from scratch, he said, the institution decided to buy an existing leasing company when it became available.

American Financial's founder, James R. DeFrancesco, will continue to operate the seven-year-old firm, the bank announced.

In addition to the leasing operation, Perpetual said it had purchased licenses to two related computer software programs developed by DeFrancesco to streamline lease and loan applications. One provides car dealers with quick information on monthly payments and other lease terms through a touch-tone phone and a computer-generated voice response. The other software program is an automated credit-processing system to allow loan officers to make credit decisions quickly.

Owen said that, with Perpetual's addition of a leasing division, the software is "a key ingredient, because it can allow dealers to respond quickly to the needs of their customers.