Signet Banking Corp., the Richmond-based bank holding company that operates throughout Maryland, Virginia and the District, yesterday reported that its profit for 1990 plummeted 66 percent to $41.4 million ($1.56 per share) from $123.3 million ($4.55) in 1989.

In the fourth quarter ended Dec. 30, the company's earnings dropped 79 percent to $6.8 million (26 cents) from $32.7 million ($1.22) in the same period a year earlier.

Robert M. Freeman, Signet chairman and chief executive, blamed the performance on the rapid decline in real estate values and a slowdown in the national and local economies, which dramatically increased Signet's troubled loans.

Loans that are no longer paying interest or are in default, known as "nonperformers," totaled $270.9 million at the end of the year, up $100 million from the level of troubled loans at year-end 1989.

In addition, Signet charged off $108.7 million in 1990, more than double the level of charge-offs recorded in 1989. Such charges are the way banks recognize loan losses that already have occurred as a result of falling collateral values or actual foreclosures.

First Virginia Banks Inc. continued to buck the trend in banking yesterday, reporting earnings of $65.1 million ($3.05) for 1990, down only slightly from its record profit of $67.3 million ($3.20) in 1989.

The Falls Church bank company, which has concentrated almost entirely on consumer lending, said it earned $15.9 million (75 cents) in the fourth quarter, compared with $16.5 million (79 cents) in the same period a year earlier.