The Securities and Exchange Commission yesterday sued First Coolidge Corp., a Watertown, Mass., bank holding company, charging it with its shareholders about its financial worth between 1972 and 1975.

First Coolidge agreed to a permanent injunction at U.S. District Court here, while neither admitting nor denying the allegations in the SEC suit.

The company also agreed to retain a special auditor to examine financial matters raised in the SEC action. The auditor will then issue a report on his findings.

First Coolidge controls one bank, which in 1977 reported assets of $138 million and deposits of $133 million.

The SEC alleged that First Coolidge:

Did not charge off uncollectible loans.

Did not maintain adequate records on borrowers.

Overstated the value of foreclosed and other property that it owned.

Violated various state and federal banking laws.*tGave preferential treatment on loans to directors.

Among several transactions in the complaint, the SEC said that in 1975, First Coolidge failed to set up a loss reserve on its books.

As a result, the company was able to show a profit of $231,000 for the year. If the reserve had been figured in, the SEC said the company would have suffered a net loss of $935,000.