Vienna Town Manager Manager John H. Schoeberlein has proposed a $10 million budget for fiscal year 1987 that keeps the town's real estate tax rate unchanged for the fourth year in a row.

But homeowners will still get a slightly higher real estate tax bill next year because of a 5.8 percent increase in Fairfax County property assessments. Vienna residents pay Fairfax County real estate and personal property taxes, as well as local real estate taxes, to help pay for schools and fire protection, which, among other services, are provided by the county.

If the Town Council, whose approval is necessary for the budget to become final, keeps the real estate tax rate of 33 cents per $100 of assessed value, a homeowner with a house assessed at $121,785, the median in Vienna, would next year pay $401.89, an increase of almost 6 percent.

During the current fiscal year, which will end June 30, that homeowner would have paid $379.50 in local real estate taxes for the same residence, which would have been assessed at $115,000.

"This is a hold-the-line budget," Schoeberlein said in a telephone interview. "With the stable community we have, we're not experiencing rapid growth like other areas in Fairfax County, and it's not necessary to greatly expand our work force."

The proposed $10 million spending program also calls for a nearly $1 million increase in the town's current $6.2 million general fund, which includes expenses for personnel, public works, parks and recreation and the police department, among others.

The proposed budget provides for a 6 percent spending increase from the current $9.1 million budget to help offset rising insurance costs for the town, a $100,000 addition to Vienna's community center, a series of public works projects and a hefty increase in the price of water, which the 15,500-population town buys from Falls Church.

"We're adding very little in new employes because we didn't get many requests from the different departments," said Schoeberlein. "Everyone seemed fairly comfortable with the current staffing levels." Vienna has about 160 full-time employes.

Because of some badly needed water and sewer line repairs and inspections in Vienna's older neighborhoods, Schoeberlein allocated $2.8 million for the town's water and sewer fund, up slightly from the current $2.7 million level.

"We're going to spend $65,000 to replace all the storm drainage pipes on Audrey's Court, which has had a severe flooding problem in the past," he said. "We're also going to increase our spending on street repaving by $50,000 . . . to stay on a decent schedule so we won't have to repave all at once."

In 1982, Vienna's real estate tax rate was increased slightly from 31 cents to its current 33 cents per $100 of assessed valuation.

Schoeberlein said he was comfortable maintaining a consistent tax rate over several years "as long as you're not faced with a major increase in spending . . . . If there's an economic turnaround you could have some problem."

The Town Council is scheduled to vote on the budget June 16.