A Washington Post poll has found that a majority of Fairfax City residents do not want the jurisdiction to quit the Fairfax County school system, which has operated city schools since 1961 when Fairfax became independent of the surrounding county.

Of more than 300 households surveyed by The Post, 55 per cent said they favored remaining with the county school system, 32 percent said they favored remaining with the county school system, 32 percent said they favored separate city schools and the rest were unsure or had not followed the issue closely enough to form an opinion.

A long dispute over school costs erupted between the two Fairfaxes last December when the county canceled the existing school contract, effective July 1979. A divided City Council has refused to negotiate a new contract with the county and begun preparations for an independent school system for the city's 4,500 pupils.

Schools since have become the major issue for the city's 21,000 residents in the upcoming May 2 election for mayor and City Council.

The Post poll found an even larger majority of residents (76 per cent) feel there should have been a citywide referendum on the school issue, something the present City Council has declined to hold.

The poll did find, however, that a majority of residents approve council decisions on other controversial questions, such as setting up a separate city fire and rescue service, vetoing a gasoline tax for Northern Virginia and withdrawing from the Metrobus system.

Further details for readers in Virginia may be found in today's Virginia Weekly.