In state legislatures from Connecticut to California, in a dozen congressional subcommittees, in a score of federal regulatory agencies, the civil liability crisis is emerging as one of the biggest policy and political battlegrounds of 1986.

The struggle has spurred some of the nation's largest political action committees to stretch for record levels of campaign contributions. It has forged a classic strange-bedfellows political alliance that finds Ralph Nader and the small-business community working together as partners.

President Reagan has created a special Cabinet council to examine solutions. One big insurance firm has budgeted $1 million for a nationwide campaign advocating creation of a special presidential commission on the crisis.

Proposed remedies vary sharply, depending on who is making the proposal. But the different responses fall into two general categories.

Insurance companies and some large manufacturing concerns are pushing for laws to restrict an injured person's right to sue for compensation and sharply limit the amount of compensation the injured party could receive. They also want limits on the fees that a plaintiff's lawyer can earn from a personal injury suit.

Legislation encompassing these limits has been introduced in almost every state legislature this year. The insurance industry also wants to nationalize product liability laws, so that manufacturers -- and insurers -- would not face different rules and standards for damage actions in each state as they do today.

These industry goals are reflected in legislation proposed by Sen. John C. Danforth (R-Mo.), Commerce Committee chairman, who has declared the liability crisis his committee's No. 1 priority this year.

The Danforth bill would largely eliminate punitive damage awards -- the source of most multimillion-dollar judgments in injury cases -- and limit compensatory damages to the victim's economic loss, with no payment for intangible harms such as pain and suffering.

On the other side, a coalition of consumer advocates (including Nader), trial attorneys and small business interests facing huge jumps in insurance fees are pushing for laws and regulations that would force insurance companies to provide coverage and limit biannual increases in premiums.

Some state legislatures have combined the two contrasting approaches. Massachusetts and Ohio, for example, have passed laws limiting insurers' liability exposure but requiring the firms to provide coverage to municipalities and small businesses.

While government entities battle over these questions, the private sector is moving ahead with its own remedies. Some business groups, including chemical firms and hospital chains, have started their own "captive" insurance companies so that they need not deal with traditional insurers.

And many state, county and municipal entities have decided to "go bare" -- that is, to operate without insurance coverage -- partly to escape large increases in premiums and partly to retaliate against insurers who are restricting coverage.

After the state of Colorado had its general liability coverage "non-renewed" this year, for example, state House Speaker Bev Bledsoe proposed legislation calling for all state agencies to drop their insurance coverage. "The next time an insurance salesmen comes around here, we'll just say, 'To hell with you,' " Bledsoe said.