The chairman of a House Appropriations subcommittee grilled D.C. Fire Chief Theodore R. Coleman yesterday on the massive overtime payments in the department's budget last year during a hearing on the District's fiscal 1987 budget.

Rep. Julian C. Dixon (D-Calif.), D.C. appropriations subcommittee chairman, said he wanted to know why "every year for the past three years" the chief projected about $500,000 in overtime costs when "you know for a fact that isn't true."

Dixon suggested that the department either project $7 million costs for overtime, which are approximately the amount the department actually spent in fiscal 1985 and 1986, or seek more personnel. In 1985, the department received supplemental funds to cover operating costs and is seeking them again this year.

Coleman responded that the department is forced to live within "a budget mark" set by the mayor's budget office when the budget is formulated, before it is sent to the City Council and Congress for review. By the end of May the department will be up to "full staffing," cutting the need for overtime, he said.

The proposed budget of $68 million for the fire department represents an increase of about $8.4 million over the fiscal 1986 budget, much of it for 80 new positions and a general 4 percent pay increase.

The department is funding a new unit to deal with incidents involving hazardous materials, rather than the current unit, which must also deal with rescues. However, the new unit will be funded for only half the year, a proposal that was criticized by one subcommittee member.

The proposed D.C. police department budget is about $158 million, which represents an increase of about $9.6 million over this year's budget, Assistant Chief Isaac Fulwood Jr. told the subcommittee. The budget calls for enhancement of the 911 emergency system and the hiring of nine new Spanish-speaking employes to "ensure 24-hour bilingual coverage." CAPTION: Picture, Theodore R. Coleman . . . projected $350,000 for overtime