District of Columbia tax officials and attorneys representing thousands of suburban white-collar professionals signed an agreement yesterday for the city to refund more than $40 million in the city's ill-fated "professional tax" on April 1, 1981.

The agreement, approved by D.C. Superior Court Judge John D. Fauntleroy, provides for the financially strapped city to mail out a single lump-sum repayment to each eligible white-collar professional -- amounting to thousands of dollars for many individual lawyers, doctors, architects and other professionals who work in the city but live in the suburbs. The refund was ordered earlier this year by the D.C. Court of Appeals after it ruled the tax violated the city's home rule charter.

The agreement represents a compromise between city officials, who wanted to extend the refunds over the course of one year, and five suburban attorneys suing the District of behalf of the professionals, who demanded the repayment immediately in one lump sum.

The D.C. Department of Finance and Revenue is scheduled this week to mail special four-page repayment request forms to all professionals who paid the tax. Under terms of the agreement, professionals who file repayment claims by Nov. 15 should receive their refunds April 1.

But yesterday, several sticky points remained unresolved in the repayment plan, making any exact calculation of the size of the refunds impossible. For one, the two sides have yet to agree whether the $4 million in accrued interest should be paid from the time the tax was orginally paid, or from the time the taxpayer first requested a refund.

Also left undetermined is the question of whether any refunds at all will be given to those who paid the professional tax in 1975 and 1976 -- the first two years the tax was in effect -- and failed to request a refund within three years of paying the tax. The city's position is that a three-year statute of limitations should apply, according to Richard L. Aguglia, an assistant corporation counsel, and those who did not already request refunds for 1975 and 1976" should be precluded from getting a refund" for those years.

Bradley G. McDonald, one of the five attorneys who successfully challenged the tax in the class action suit, said there is a "significant amount of money involved" in repayments for those two years that the city now considers closed cases. McDonald said that he would consider appealing that one point to a higher court, should Judge Fauntleroy rule in favor of the city.

Also still unsettled is the payment of up to $2.2 million in attorneys' fees the five suburban lawyers are requesting. The judge must still decide how much if any, of those lawyers' costs should be deducted from the refunds to professionals.

The two sides are set to meet again in court in late December to begin hammering out some of these remaining differences. In the meantime, attorneys for both the city and the professionals are urging those who paid the tax to return the repayment request forms, even though the exact size of the coming refunds is still uncertain.

Regardless of those open questions the final agreement could represent a substantial repayment to a white-collar suburban professional who paid the tax since it was levied in late 1975. Until it was struck down earlier this year, the professional tax had added $58 million to the cash-strapped. District government's coffers.

The tax was levied at a 9.9 percent rate of 30 percent of the affected taxpayer's net income. Professionals who were District residents also paid the tax, but they were allowed a check-off and deduction on their District of Columbia income tax returns. So in reality, the professionals who lived in the suburbs and worked in the city paid the bulk of the tax, making it what suburban critics said was a thinly disguised commuter tax, which is illegal under the home rule charter. That is precisely why the court threw the tax out.

Attorneys have estimated that a hypothetical professional under the tax with a net income of $50,000 annually who paid the tax for five years would be entitled to a refund of about $7,500 plus $900 in interest -- a total of $8,400 -- assuming he or she is allowed a refund for 1975 and 1976 and assuming interest is calculated from the beginning of payments. From that repayment could also be subtracted a percentage for attorneys' fees, depending on the outcome of the December hearing.

If that same professional had claimed the professional tax as a deduction from his federal income tax returns, he must, upon receiving the repayment, either recalculate his federal returns for those years, or claim the refund as new income for 1981, and pay federal income tax on the refund, city tax officials said.