Federal officials are trying to arrange a merger between the financially troubled County Federal Savings and Loan Association of Rockville and a District savings institution.

Under a takeover, County Federal accounts would be transferred automatically overnight to any S&L that acquires it without interruption in service or availability of funds, while branches of County would open under the name of the acquiring institution.

The involuntary merger, if it occurs, would be the first involving a large Washington-area financial institution in recent decades and the first interstate merger of an S&L in a generation.

The Federal Home Loan Bank of Atlanta, which has jurisdiction over the Washington metropolitan area, has invited several large savings and loan institutions in the District, Maryland and Virginia to a meeting Friday to discuss bids for County Federal, informed sources said yesterday.

County Federal has seven branches in the Washington suburbs and assets of $143 million. County Federal President Robert N. Reeves and the S&L has been trying to find a merger partner for several years.

Reeves stated emphatically in an interview this week that County Federal is still a viable institution. "We're still paying our bills," he said. Reeves acknowledged that County has incurred some temporary loan losses from building contractors who have gone bankrupt during the current period of high inflation. "But these are viable projects that will be sold when the economy comes back," he said.

One of the builders is Cowan and Hodgkin, which filed for reorganization under Chapter 11 of the bankruptcy code Feb. 17. County originally financed nine houses and five lots for Cowan and Hodgkin in the Potomac area. Nelson Cohen, an attorney for the builder, said all but one house and four lots have been sold, and the loans from County paid off.

Reeves declined to reveal financial details, but did confirm that the association's reserves now are below the required 4 percent of liabilities, a standard set by the Federal Savings & Loan Insurance Corp. (FSLIC), a government agency.

He also confirmed that these reserves include amounts set aside for possible loan losses.

Reeves said, however, he did not expect that the amounts set aside would be depleted by actual defaults. He noted, for example, that several house sale contracts have been signed daily in the last three weeks. He expressed confidence that County could recover on its own, and he hoped that an involuntary merger would not be necessary.

For D.C. savings institutions, such a merger would open a door that has been closed to them since 1955 - the chance to move into the affluent suburbs. Several years ago these savings and loans, led by Perpetual American, petitioned the Federal Home Loan Bank Board, which regulates federally chartered S&Ls, to allow them to acquire or establish branches in Maryland and Virginia. The petition is still in limbo, pending a determination of Reagan administration policy on the whole controversial issue of interstate branching.

Thwarted in his first attempt, Perpetual Chairman Thomas J. Owen recently wrote the Bank Board again, this time threatening to bring suit if the regulators did not allow District institutions to bid for County Federal. Owen charged that the FSLIC, which supervises mergers, would be acting unwisely if it did not permit D.C. firms to bid.

Given their eagerness to branch across the state line, the District-based S&Ls would presumably be willing to offer the FSLIC more favorable terms for taking over County than would Maryland S&Ls. The Bank Board's action in admitting D.C. institutions to the bidding reportedly follows unsuccessful attempts by FSLIC to arrange a merger with a Maryland S&L.

In addition to Perpetual, those District institutions invited to the meeting Friday include Columbia First, National Permanent, Interstate and Washington Federal. None of the chief executives of these institutions had yet had time to study County's loan portfolio, which was made available yesterday to FSLIC. So none could estimate County's financial position or say with certainty if his institution would bid.

A supervisory merger is an alternative to liquidation of a failing institution, a distasteful and costly procedure FSLIC tries to avoid. In case of a failure, depositors' accounts are insured up to $100,000 each. The insurance mechanism is not triggered by a supervisory merger. This means, in effect, that all deposits including those over $100,000 would be totally covered by the merger partner.

Financial institutions have the right to require a 30-day waiting period for time deposits. However, in practice, instant withdrawl is the rule. Moreover, the government customarily makes sure adequate cash is available for withdrawals.

"So, nothing is going to happen," said an attorney for County. "No one will lose any money unless they bring it on themselves." He was referring to the penalties depositors have to pay if they withdraw their funds before the maturity date.