E. F. Hutton & Co. yesterday paid a $350,000 fine to the State of Connecticut as part of an agreement to end disciplinary proceedings that arose from a multibillion-dollar check-kiting scheme the brokerage firm engaged in from 1980 to 1982.

The giant securities firm also will be prohibited from signing up new customers in Connecticut from Feb. 18 until March 3 and was put on a year's probation, during which it must file quarterly reports with the state.

Connecticut and several other states began their own investigations of Hutton after the brokerage firm pleaded guilty in a federal court last May to 2,000 felony counts of mail and wire fraud.

The counts involved a Hutton cash-management scheme in which at least 20 of the firm's 400 branches regularly withdrew more money from their bank accounts than the branches had on deposit. In effect, the banks unwittingly were making interest-free loans to Hutton. Hutton's Hartford branch was one of those involved in the checking scheme.

Hutton paid a federal fine of $2 million and $750,000 in court costs. It also agreed to make restitution to the banks it defrauded.

The Connecticut fine is the biggest state penalty the brokerage firm has paid. In addition to Connecticut, Virginia, Georgia, New York and Ohio have taken action against Hutton.

Connecticut Banking Commissioner Howard B. Brown said that $150,000 of the fine would cover the costs to Connecticut of conducting the probe into Hutton's operations and the remaining $200,000 would be donated to Connecticut charities. A spokeswoman for the the Banking Commissioner's Office said Hutton wrote the state a check for $350,000 yesterday afternoon.

Robert C. Clark, who ran the Hutton Hartford office during the years the office was part of the check-kiting scheme, had his broker-dealer license suspended by Connecticut for six months. Clark was removed by Hutton as head of the office last year.

Hutton executives have contended that the check scheme was carried out without the knowledge of top officials of the giant securities firm. The Justice Department, which investigated Hutton for nearly three years, did not require any Hutton employes to plead guilty to fraud charges, only the company. Justice has been criticized in Congress and elsewhere for failing to go after individuals, but Justice officials said the individuals the government could prosecute successfully were low-level and that it was more important to obtain the Hutton guilty plea in a case that they felt might be difficult to proscecute.

The Securities and Exchange Commission last October agreed to a consent order with Hutton in which the brokerage was barred from opening new offices for six months.

Besides the fine and the 10-day suspension of new business, Connecticut also required the company to write letters of censure to its officials who did not supervise Hutton cash-management operations properly, and prohibited Hutton from using exemptions in securities laws that enable it to short-circuit some securities laws for customers who want to raise capital by selling securities to a small group of private individuals.

That requirement means Hutton likely will lose so-called private-placement business in Connecticut for the next 180 days.

The consent order also requires Hutton to tell its Connecticut customers that they have the right to be paid with checks drawn on a local bank rather than banks hundreds or thousands of miles from Connecticut. Companies often pay with checks drawn on distant banks because it takes the checks longer to clear through the banking system and permits the check-writer to hold on to the funds longer.