State legislators in Michigan yesterday faced a political nightmare that is becoming increasingly prevalent around the nation.

With 650,000 people in the state out of work and thousands more receiving reduced paychecks because of union concessions to the auto industry, they were having to explain an income tax increase and a drop in the state's credit rating which officials fear may make it impossible for the state to borrow money to finance education next fall.

Such occurrences have become almost commonplace this year as state after state, particularly in the hard-hit Midwest, has been thrown into a budget crisis by the recession.

According to a new study by the National Conference of State Legislatures, 22 states have already increased taxes this year, nine have significantly cut the number of state employes, eight have made across-the-board budget cuts, and dozens of others have made selective budget reductions.

The actions in many cases make the budget battles under way in Washington seem minor by comparison, according to many legislators.

Minnesota levied a 7 percent surtax on personal income for one year, according to the study. Washington state increased all taxes, except property and non-general fund taxes, 4 percent for one year. Iowa, Nebraska and Wisconsin raised corporate tax rates.

Tennessee raised its severance tax on oil and gas. Seven other states raised the excise tax on tobacco, according to the study. Arizona, Idaho, Maryland, Kentucky, Vermont and Virginia raised various excise taxes.

The situation in Michigan, where the recession has been severe for more than two years, is especially difficult. The April employment rate stood at 15.5 percent, more than 6 percentage points higher than the national average.

Faced with massive budget deficits, the Michigan legislature on Tuesday voted to increase state income taxes from 4.6 to 5.6 percent for a six-month period, ending Sept. 30. This put the tax rate at a record high.

Yesterday the state's credit rating was dropped to the lowest level of any state in the country.

"Persistent and severe recessionary conditions continue in Michigan and are reflected in revenue performance and expenditure pressure," Moody's Investor Services Inc. said in a statement explaining the move. "Economic assumptions of late 1981 have not materialized and substantial recovery for the remainder of the state's fiscal year is increasingly doubtful."

State budget director Gerald Miller said the lowered ratings would increase interest costs on bond sales, jeopardize state plans to borrow $500 million and threaten the finances of schools and local governments.

"We feel like someone with three kids in college and a sick mother, who has just been laid off and found his checkbook is $5,000 overdrawn," said one legislative aide.

The Michigan situation is hardly unique, however. States across the country have watched their tax revenues shrink during the last year as costs related to welfare and to unemployment have increased. Two-thirds of the states responding to a survey by the Federation of Tax Administrators last December reported tax revenues were running behind projections.

This has resulted in repeated confrontations, and patchwork remedies. In Idaho, 5,000 state employes have been put on a four-day work week. In Wisconsin yesterday, officials of unions representing 28,000 state employes rejected a request that they accept a three-month delay in salary increases.

Even oil-producing states, such as Louisiana, which boasted "an embarrassment of riches" two years ago, have encountered problems. About 40 percent of the state's income is tied to oil, but revenue has fallen far below expectations.

Gov. Dave Treen has trimmed his budget by $119 million, and called for a new oil and gas tax--the largest in state history--to met the state constitution's requirement of a balanced budget.