This city's financial future, as well as the political career of its youthful mayor, will be on the line Tuesday as voters decide whether to sell the Municipal Light and Power Co. (Muny Light) plant and raise the city income tax 50 percent.

A double-headed victory for Mayor Dennis J. Kucinich -- that is, a vote to keep the plant and increase tax -- would strengthen him politically not only for this year's elections but also in his war against the city's power structure.

Kucinich, 32, has made the Muny Light plant the symbol of his political independence.

A double loss could further cripple Kucinich, who escaped a recall attempt last August by only 236 votes out of 120,000 cast.

"I think the Muny Light question, for the most part, is a test of his own strength," said Timothy F. Hagan, a Kucinich foe and county Democratic Party chairman.

While the city would profit somewhat from the sale of the light plant it would not be enought to dent the massive deficit facing the city this year.

City spending controls modeled after the Emergency Fiscal Control Board established in Yonkers, N.Y., three years ago, have been introduced in the Ohio legislature, but action has been delayed pending the outcome of Tuesday's voting.

Several weeks ago, polls showed the income tax raise would pass easily and voters would decide to sell the light plant by up to a 70 percent majority.

However, a respected Cleveland pollster said late last week the tide apparently has turned on the Muny Light issue as a sampling of 500 persons showed the sale would be defeated by 55 to 45 percent.

The poll was taken after reports in both daily newspapers that the privately owned Cleveland Electric Illuminating Co. (CEI) had schemed to drive the city-owned plant out of business.

Kucinich also appeared to have capitalized on actions by the business community. Twice in the past two weeks corporation heads have met behind closed doors reportedly to discuss how to deal with Kucinich politically. News leaks prompted Kucinich to point to this as evidence that big business was out to get him.

Also, two weeks ago, CEI announced that it would seek an increase of up to 25 percent in the cost of the wholesale power it sells to the city, an increase that would be passed on to Muny Light customers. Kucinich said this was further evidence of CEI's price gouging.

Kucinich has campaigned extensively for the city to retain Muny Light, saying that CEI and the Cleveland Trust Co. conspired to force the sale by pushing the city into default last Dec. 15. Cleveland Trust holds $5 million of the $14 million in defaulted notes.

Consumer advocate Ralph Nader is featured in one of five commercials Kucinich has aired on television. A sixth, which implies that CEI and Cleveland Trust executives were crooked, was rejected by two of three television stations after the lawyers advised they might be libelous.

Kucinich said Cleveland Trust Chairman M. Brock Weir insisted the city sell the light plant as a condition for the refinancing of city loans Dec. 15. Weir has denied that.

Five other banks were prepared to continue the city's credit but did an about-face when Cleveland Trust said it would call in the loans.

Following official complaints by Kucinich, the Securities and Exchange Commission, Federal Reserve Board and the antitrust division of the Justice Department launched investigations into the light-plant default issue.

Kucinich is clinging to Muny Light to protect the city's $330 million anti-trust suit against CEI. The trial was to have started this month but has been indefinitely delayed.

Even light plant foes have said the antitrust case has merit and should be prosecuted.

"But, it could drag on for six years," said Councilman Michael White, who supports the sale because he believes the plant will sap the city of $50 million in subsidies by the time the case is settled and "there are no guarantees the city will get a dime."

Tuesday's ballot calls for Muny Light to be sold for at least $158.5 million, the amount offered by CEI before Kucinich canceled the deal after taking office in 1977.

As a condition of the sale, CEI insisted the antitrust case be dropped.

If the plant were sold, the city would get $38.5 million immediately and $120 million over 30 years, but Muny Light's debts would use up all but $9 million of the down payment, said Law Director Jack Schulman.

Projections of the city's deficit this year range from $55 million by Kucinich to $100 million by County Auditor Vincent C. Campanella.

The mayor said increasing the income tax from 1 percent to 1.5 percent would generate $25 million in additional revenue this year and $38 million in 1980. If the city could not market a debt consolidation bond issue, he would use the tax proceeds to pay off the defaulted notes and then refund $41 million to a capital improvements fund that had been raided for operating expenses in the past.

The city also has $25 million in other notes coming due this year and Kucinich is hoping to repay them with proceeds from the bond issue.

An administration cash flow projection shows the treasury going broke some time next month. Kucinich has said city services will be drastieally cut if the tax increase fails but has hedged on exact figures because he said he does not believe in scaring voters into approving the higher tax.

After the city's default on its notes in December, Kucinich said he would have to lay off 3,500 city employes, or 35 percent of the work force.

Waiting in the wings is the state government, which agreed not to take any action until after Tuesday. Last year, a premature promise of emergency state aid for schools was blamed for the failure of school levies to be approved.

There are two state plans already proposed. The first, submitted by Gov. James A. Rhodes, a Kucinich foe, calls for the formation of a nine-member commission that would strip the city of much of its budget authority.

It would authorize the state to make loans to the city and impose strict accounting mechanisms to safeguard against misspent bond funds.

The second plan, drafted by the Kucinich administration, would allow the state to appoint a fiscal agent who would be a watchdog against misspent funds but would not make budget decisions. Kucinich's plan also calls for state loan authority and tighter fiscal controls.

State Rep. Harry J. Lehman of Shaker Heights said no matter what the outcome of Tuesday's vote on the higher income tax, there is likely to be a compromise approved by the state legislature as an effort to restore investor confidence in Cleveland so it can once again market bonds.