The recent trend toward proposed interstate bank mergers continued yesterday as the Girard Co., parent company of Philadelphia's Girard Bank, announced it would purchase control of Farmers Bank in Delaware for $38.6 million. The State of Delaware currently owns a controlling interest in the bank.

The Girard transaction, made possible when Delaware officials accepted the Philadelphia bank's bid from among five submitted in recent days, differs from those proposed by Citicorp, Chase Manhattan and Marine Midland, which have made plans to invest in out-of-state bank firms.

Whereas these New York institutions cannot open full retail branches in other states without a change in federal law, the Girard-Farmers merger can probably skirt the Douglas amendment to the McFadden Act, which prohibits bank holding companies from making acquisitions or opening branches across state lines. A provision in that act allows state legislatures to override the federal law by passing statutes specifically authorizing interstate mergers.

A number of states have reciprocity clauses with other states, allowing banks to branch in each other's jurisdictions. Delaware does not, but its General Assembly is expected to pass legislation to permit just this particular merger. The reason is that Delaware, which owns 77 percent of Farmers, would like to get out of the banking business. During the first half of 1981, Farmers had net income of $4 million, down from $5.1 million in the same period in 1980.

Farmers, with assets of $500 million, is one of only two state-owned, full service banks in the country; the other is the highly successful Bank of North Dakota. The Delaware bank has been for sale for a decade. When it faced a crisis in 1976, Delaware and the Federal Deposit Insurance Corp. gave it cash infusions. Three years ago the bank's minority stockholders, together with management, tried unsuccessfully to raise enough capital to buy Farmers from the state. So competitive bids were invited and Girard's was the highest of five bids.

Girard has offered $23.25 per share of common stock. If the merger is approved by the Delaware legislature, the FDIC and bank regulators, Farmers will become a subsidiary of a Girard holding company chartered in Delaware.