The Prince George's County school board Thursday night approved a $249.7 million budget for 1977-78 that is $4.9 million over the spending limit proposed by County Executive Winfield M. Kelly.

School Supt. Edward J. Feeney described the budget, which represents a 7.2 per cent increase over current spending but calls for no new programs, "very tight."

Last year a heated dispute between the board and Kelly culminated in an effort - later abandoned - by the executive to wrest control over scool spending from the board.

But according to Kelly aide John A. Lally, this year the executive expects to work out a reasonable solution to any differences over school spending. He said communications between Kelly and the board are much better than in the past.

The 1977-78 budget, which now goes to Kelly, provides for 6 per cent raises for most school employees. Contracts with three employee bargaining agents call for an annual cost-of-living raise up to a ceiling of 9 per cent based on increases in the consumer price index.

The 6 per cent budget figure is based on an estimate and would be adjusted based on the Washington area index to be reported next month.

The budget also calls for removing by attrition 188 positions from the system because the student population is declining. A school spokesman said the deletion of the 188 positions will save thecountry more than $2.6 million in the next year.