The calamity that federal financial regulators fear most--a run on the bank--occurred this week at a Connecticut savings and loan association.

In a two-day period, panicked depositors withdrew more than $3 million following a newspaper article stating the institution had suffered a $7.3 million loss and would be merged out of existence.

In an ironic coincidence, the National Broadcasting Co.'s television network last Sunday evening aired the movie "The Day the Bubble Burst," a saga of the Wall Street crash of 1929. The film shows crowds lined up outside a closed bank chanting: "We want our money."

Barbara French, a reporter for The Hartford Courant who interviewed customers withdrawing funds from the Hartford Federal Savings & Loan Association, said they told her the movie had frightened them. Elderly people recalled bank failures during the Great Depression, she added.

Hartford Federal Chairman Christopher W. Carriuolo went on local television to reassure customers that there was no need for concern about the safety of their deposits because their funds are insured by an agency of the federal government for up to $100,000 on each account. He attributed the run to a Courant article which led the paper Saturday morning.

Under a headline "Merger Possible After Bank Loss," the article said that Hartford Federal had suffered a loss of $7.3 million in 1981, the largest loss by any Connecticut S&L. That reduced its net worth or reserves to $1.3 million, far below the federally required minimum of 3 percent of liabilities. Hartford Federal had $365.8 million in deposits insured up to $100,000, the newspaper noted. The article added that the Federal Home Loan Bank Board was searching for a merger partner for the troubled S&L and that its major asset--the city block on which its headquarters is located--was being sold.

Carriuolo could not be reached yesterday by telephone. French, who said Hartford Federal officials no longer returned her calls, quoted other Connecticut savings and loan officials as saying the panic has abated, but not before withdrawals reached $4-5 million.

The bank board, which declines to discuss individual cases, had no comment yesterday. In an effort to preserve public confidence in S&Ls--and avoid the type of incident that occurred in Hartford--regulators no longer openly acknowledge how many savings institutions are in trouble.

Based on an analysis of mid-1981 data, The Wall Street Journal has projected that 200 are in danger of failing. It quoted an unnamed official this week as saying that 40 troubled S&Ls are expected to be merged into healthier ones this month. Thus far in 1982 there has been an average of one supervisory merger a week, some of them involving several ailing S&Ls.

Last week the savings industry testified before a Senate subcommittee in favor of a bill to facilitate the sale of low interest rate mortgages to investors who would have the right to claim tax losses. In this way S&Ls and mutual savings banks hope to get rid of their old mortgages and use the funds for making new mortgages at higher rates or for other types of investments.

The U.S. League of Savings Associations claims its members have some $300 billion in low-yield loans on their books. The Joint Tax Committee has estimated allowing investors to buy them for tax losses would mean a drain of $30 billion on the Treasury. The Treasury, which last week opposed the bill as bad tax policy, put the revenue loss at $50 billion.

Emergency legislation to aid mutual savings banks and savings and loans passed the House last fall, but it is stalled in the Senate, where the banking committee chairman wishes to make it part of a comprehensive reform of the financial services industry.