HARTFORD, Conn. (AP) _ A new system to handle disputes over auto accident claims may ease pressure on overcrowded courts and bring speedier resolutions, a major insurance company says.

''It's one of those things where everyone wins,'' said Henry J. Naruk, vice president and associate general counsel of the Hartford-based Travelers Cos., which is launching the program.

''If we get a lot of the routine stuff out of the courts, they get more time for the things that take longer,'' he said.

In a year-long test to begin this fall, Travelers will set up a Hartford center as an alternative for litigants in Connecticut automobile accident cases involving personal injury and property damage claims of up to $50,000.

If it works, Naruk said Travelers would like to make the center a non- profit, self-supporting corporation.

The company will hold an organizational meeting Tuesday for potential participants, including 12 major insurance companies.

Auto accidents with claims under $50,000 make up the bulk of Travelers' claims, according to company statistics. They represented 91 percent of the cases settled nationwide by the company in the first six months of 1986, a Travelers spokesman said Monday.

The center will be open to other insurance companies, independent arbitration and mediation businesses and lawyers representing any side of a case, Naruk said.

Participants will be able to choose a variety of options, such as mediation, arbitration and mini-trials, he said.

An accident case involving bodily injury may stay in the Superior Court system in major Connecticut cities for an average of three to five years, Naruk said. The alternative center may handle cases in from a day to several months, he said.

Litigants not satisified with the suggested settlement may take their cases back to the courts, Naruk said.

Travelers and other companies already have programs offering some alternatives to going to court, Naruk said. However, the center will be unique, in part because of its flexibility in accepting and settling qualifying cases from any part of the industry, he said.

''If we can make this work, we will apply it to other jurisdictions (or states), said Naruk, a former state Superior Court judge.

Center cases need not have been filed in court, although the project will take lawsuits already in progress. Naruk said he could not estimate how many cases the center would handle in the trial year.

David Jackson, the civil case flow manager for the Connecticut court system, said the number of pending civil cases was decreasing but needs further reduction.

As of June 30, 13,853 civil cases were awaiting jury trials and 4,011 were holding for bench trials, he said. Those numbers were down from a peak several years ago of 16,400 on the jury trial list and 13,003 on the court trial list, he said.

Jackson credited a number of new programs designed to settle cases out of court with reducing the court load.