The warm spring wind that came early to the Magnolia State this year has blown political storm clouds over the ornate domed Capitol.

In this contradictory place, where outward signs of an integrated New South exist with vestiges of a separate society, evidence of change abounds, and not only in the season: In the lobby of the downtown Jackson Holiday Inn, a white woman shines the shoes of black customers. On the television sets in its rooms, black and white reporters anchor evening news programs side by side.

"In many ways, the people here have handled integration much better than in the northern cities that criticized them," said Jack Lynch, a transplanted Missouri farm boy who is now spokesman for the Mississippi Department of Education.

The price of change here has been high, however, in a state that ranks last in per capita income, per-pupil expenditures and literacy. The bill for Mississippi's traditional neglect of its public sector is coming due, pitting Gov. Bill Allain against the legislature and the state's teachers against both.

The tempest began last week when a state court found this cash-strapped state in contempt because of prison overcrowding and gave Allain until May 1 to correct the problem.

Also last week, Allain confronted the legislature head-on for the first time by vetoing its bill to fund the state Treasury Department in fiscal 1986. Allain, a self-styled anti-tax populist, said it was more than Mississippi taxpayers could afford, and lawmakers are trying to marshal votes for an override.

At the end of the week, a new crisis hit the statehouse when FBI agents entered the Capitol and arrested State Sen. Tommy Brooks, president pro tem of the Senate, on charges that he extorted $50,000 from horse-racing tracks. Brooks has declared his innocence.

This week, a teachers' strike that began in the southern part of the state spread through a quarter of its school districts, as teachers converged on the capital with posters and pennants demanding an end to their status as the nation's lowest-paid educators.

Mississippi's House members, faced with a mounting budgetary crisis that could only be aggravated by the teachers' demands, reacted by voting to raise their own pay and increase their retirement benefits.

To make bad matters worse, Jackson city elections planned for mid-May were thrown into confusion this week when the U.S. Justice Department raised last-minute questions about new ward boundaries that would create three majority-black districts, three majority-white districts and one "swing" ward.

The department has asked for minutes of City Council meetings to review whether ward lines were drawn up with racial motivation, and city officials fear that the elections for mayor and council could be delayed.

The action, taken under the 1965 Voting Rights Act, came as Mississippi, symbolically at least, seemed to be shaking off its past. As city officials were assessing its ramifications, a black judge was being sworn in for the Hinds County Circuit Court, replacing a judge who left to become the first black on the Mississippi Supreme Court.

But as the teachers' strike so dramatically underscored, public policy and political debate here are scrutinized for racial overtones. In education, they are stark, with many white Mississippians, particularly in the more conservative northern half of the state, shunning the integrated public school system in favor of private, predominantly white academies.

In the face of closed schools and hard choices that may include a tax increase, however, Mississippians know a crisis when they see one: Their most pressing concern lately seems to be that the strike might disrupt the state's high school basketball championships now under way.

"We know those people up in Washington laugh at us," Lynch told a visiting Washington reporter. "But you tell them one thing. We may be last in the country in everything, but when we get ready to buy a 3-cent bolt, we pay 3 cents for it, instead of $300 for it like they do up there at the Pentagon."