The Washington Post reported that Richard Gordon Hatcher of Gray, Ind., "won the title of first black mayor of a major city" when he was elected in 1967. In fact, Carl B. Stokes, who is also black, was elected mayor of Cleveland that same day. CAPTION: (NEW-LINE)Pictures 1 and 2, Jesse Bell, left, is challenging Mayor Richard Hatcher in the Democratic primary.

Like a final exam in Urban Studies 101, tomorrow's election in this grimy, rundown city poses a single trying question: Given $500 million to work with, how would you save an urban derelict?

Mayor Richard Gordon Hatcher, who is seeking nomination for a fourth term in the Democratic primary here, answers that question - as he has since he took office 12 years ago - by saying that Gary and cities like it need big money poured into big projects.

"When you've got a dying city you've got to build," Hatcher says. "I've gotten about $500 million in federal grants, and we've used that to build decent housing for our people, and centers for our seniors, and vocational schools to teach these kids a trade. That's the kind of thing that you need here."

Hatcher's opposition sees thing diferently. Dozier Allen, leader of a group of black Democratic dissidents seeking to unseat the mayor, says: "King Richard has used that money the wrong way."

"I say the man's got to run the city, day to day," Allen declares."I say he's got to increase police patrols instead of laying off cops. He's got to buy some fire trucks that work, so our insurance rates will come back down. I say, if he spent $500 million here, how come people's garbage doesn't get picked up?"

Hatcher acknowledges that his administration of routine city functions has "not always been perfect," but he thinks the city's 170,000 residents - or at least the 55,000 of them who are expected to vote - will continue to back his priorities.

He's probably right. Allen, who is probably the city's second most popular politician and who gave Hatcher a fairly tight race in the 1975 mayoral primary, did not run this year. It didn't look very promising, he explains.

Instead, Allen and other dissidents recruited Jesse Bell, a former Hatcher confidant, to challenge the mayor in the Democratic primary, which is the only real election contest in this heavily Democratic town.

Bell, a bearded, outspoken 56-year-old black, has put on a vigorous campaign and seems to have the self-assured mayor slightly worried. But Hatcher, who has access to money and publicity far beyond what Bell can command, is a strong favorite.

Ever since his upset election here in 1967 won him the title of "first black mayor of a major city," Hatcher has had close ties with the black liberal establishment nationally. This year, blacks across the country have contributed to his campaign. He will spend about $125,000 - five times Bell's budget - and such friends as Jesse Jackson, Dick Gregory, Coretta Scott King, and Los Angeles Mayor Tom Bradley have backed his candidacy.

In addition, the Carter administration has handed Hatcher two public relations coups by announcing, within a month of election day, two major grants for rebuilding downtown Gary. The administration says the timing was coincidental. But to reinforce the message of official support, Vice President Mondale, who rarely takes sides in primary elections, flew here last week for a Hatcher fund-raiser.

Hatcher, a smooth 46-year-old whose tailored suits, monogrammed shirts and designer sunglasses make him look like Hollywood's idea of the successful black businessman, says most Gray residents are proud that their city has produced a national figure.

What Gray produces mostly, though, is steel. Founded by the U.S. Steel Corp. in 1905 and named for the company's chairman, Elbert H. Gary, the city's reason for existance has always been the U.S. Steel complex that sprawls for miles at the edge of town beneath an ever-present blanket of soot and steam.

Like other steel mill towns, Gray has always been a drab, dirty place. In the past two decades, though, the general dreariness has been accentuated as middle-class flight and business departures have given the downtown and many neighborhoods the appearance of a boarded-up ghost town.

One of the debating points in the current campaign is whether Hatcher has been effective in stopping the process of decay.

Bell and his mentor, Allen, contend that things have gotten worse in the dozen years since Hatcher took over.

"Twelve years ago, you could get a presciption filled in this down at night," Allen says. "Now you have to leave the city to find a drugstore open. You have to leave the city to find a movie theater you can take your family to."

They argue that Hatcher has slighted daily municipal operations to focus on grantsmanship and big building projects. Last year, for example, the mayor spent nearly a million dollars of general revenue-sharing funds - money that many cities use to buy equipment or pay city workers - on architectural studies for a new civic center.

Then during last winter's deluge of snow, the city had only 16 snowplows available to clear its 4,500 residential blocks. Bell calls this "outrageous." Hatcher, who minimizes the impact of the snow, says he would not hesitate to use his revenue-sharing money for architecture rather than snowplows if he were faced with the decision today.

The other question in this election pitting black against black concerns which side is "racist."

Hatcher said last week that much of his opposition stems from a feeling that "a black mayor shouldn't be allowed to succeed." A center of that sentiment, he says, is the local newspaper, which the mayors calls "racist" - a charge that infuriates the paper's black city editor.

Bell, meanwhile, accuses Hatcher of "blatantly racist" polices that have "scared the white people out of town." Allen, who is overseeing Bell's campaign, agrees, saying that Bell can win if he gets "all the white votes in this city and the 40 percent of the blacks who don't want to see a racist in city hall."