In the two months since Prince George's County voters approved his property tax-freezing TRIM charter amendment, William J. Goodman, champion of the overburdened homeowner, has begun his next project. He is trying to force county apartment owners to pay a larger share of taxes.

Assisted by a loyal band of businessmen, housewives, and students, Goodman has formally challenged the asessments on 126 apartment complexes in the county. By July 1, he hopes to force county officials to reassess 60,000 individual apartment units at the higher market value of condominiums.

If he is successful, homeowners in Prince George's could get a substantial reduction in their tax bills next year -- perhaps much as $75 to $100 -- while apartment renters in Prince George's and, perhaps, throughout Maryland would pay an average $230 a year more in rent, according to Goodman's figures.

More importantly, Goodman, the most successful and well-known gadfly in Prince George's County, will have won another victory for his ideals -- "equity and accountability" -- despite the attacks and putdowns of bureaucrats, and "special interests."

Cheered on by a small, army of middle-class citizens who see him as a leader of the common property owner, and as the graying undaunted Howard Jarvis of New Carrollton, Goodman says, "I don't feel like a hero, I've done this before."

Already, lines are drawn: county officials are saying that Goodman's campaign is hopeless and misguided; Goodman is arguing that he is following the Constitution.

Goodman has printed up TRIM (for Tax Relief for Marylanders- stationery and T-shirts, has prepared a direct-mail solicitation, and has recruited volunteers to sell 3,000 TRIM membership cards at $5 apiece.

Before he is through, Goodman expects that he will exhaust $10,000 in legal fees taking his case to the Maryland Court of Appeals, and that he will be attacked and discounted by every developer and tax assessor in the state.

In fact, Goodman seems to be doing what he enjoys most. "When he makes up his mind on an issue," said Del. Frank Pesci, who worked for Goodman in the 1960s, "it becomes like a beacon to him and he just keeps driving for it. You can beat him over the head and it just slides off."

Before taxes, Goodman's beacon was the environment. This was in the 1960s when Goodman was a delegate in the Maryland legislature and when, as Pesci said, "Nobody but him cared about any of those things."

Goodman played a major role in passing state strip-mining and land-use acts, in addition to measures helping to preserve the Patuxent River watershed and the Eastern Shore wetlands.

He is proud of it: "As a legislator," he says, "I was the most effective environmentalist in the country."

Goodman was defeated in a reelection bid for the State Senate in 1974, however, then beaten last fall when he tried again. But at 47, he has found another cause, and he has no intention of giving it up.

There is only one problem. Goodman and his supporters, according to various county officials, don't understand tax assessments. What's more, these officials say they aren't very good at mathematics.

When Goodman and his runningmate, David Bird, introduced Prince George's to TRIM last June, they said that freezing the county's tax collections at $140 million would eventually reduce tax bills for homeowners as more land in the county was developed.

It was not until voters approved TRIM that county officials -- and TRIM's backers -- realized the freeze would not reduce taxes for most homeowners because the assessment value of single family homes rises faster than that of apartments and businesses.

Goodman is arguing that because there is a market for apartments that are sold as condominiums all apartment complexes should be assessed at the value the owner would receive if he were to sell his ownings unit by unit, as condominiums. Currently apartments are assessed according to the value the sale of the entire complex would bring, a much lower price.

According to TRIM's figures, the average apartment unit in the county is assessed at $5,500, while comparable condominiums are assessed at $12,000. This discrepancy is not fair, Goodman maintains, because apartments and condominiums have identical zoning and because often condominiums are little more than apartments that have been sold to their owners.

But Harry S. Shipp Jr., the county's chief tax assessor, points out that assessments are supposed to be based on the market value of the property. The assessments of the apartments Goodman cites, he says, are based on sales of those apartment complexes from one owner to another in recent years.

County officials also say that if Goodman's method of assessment were followed, apartment owners would actually pay more taxes than condominium residents, because under state law, apartments are assessed at 50 percent of value, while resident-owned properties are assessed at 45 percent of value.

Further, Goodman's estimates of a potential $25 million increase in county property tax revenues under the assessment change -- and a resulting 50-cent tax rate cut -- are predicated on obviously erroneous calculations, officials say.

Goodman admits that his figures are cloudy, but he promises that his case will be tightened before it reaches the courts -- where he expects that his appeals will be heard.

He will not give up easily. "These people like Shipp think we're playing games with them," he said. "But they are going to find out how serious we really are."