Stockholders of James Madison Ltd., the holding company that owns Madison National Bank, yesterday approved a two-for-one stock split that increased the number of shares outstanding to 820,000.

By halving the price and doubling the number of shares, the split should increase the market for the stock, said Chairman K. Donald Menefee.

Madison's profits were up 26 percent in the first quarter, but "we do not necessarily feel that we will be able to maintain this pace for the balance of 1982," Menefee told stockholders at the annual meeting. "Future performance will depend greatly on the performance of the economy and the Federal Reserve's reaction thereto."

Menefee said Madison Bank so far has less than $400,000 in "nonperforming," or past-due, loans, less than 0.3 percent of its loans. But he noted that the holding company has been unable to find a tenant for two-thirds of the rental space available in its new Georgetown office at 29th and M Streets NW.

The holding company has $2.8 million invested in the property, which "at this time would have to be classified as nonperforming, or at least partially nonperforming," he said. The bank occupies the ground floor of the building, but the office space on the second and third floors and four of the five apartments atop the offices have not been rented.