The Arlington County Board yesterday adopted a $168.8 million budget that manages to cut real estate and automobile tax rates and give the county's 2,400 employes pay raises of at least 5.5 percent.

Yesterday's 16 cent cut in the real estate tax rate gives Arlington the lowest property rate in the metropolitan area and means that the average homeowner will pay about the same amount in county taxes as last year despite an average 13 percent rise in assessments.

Under the new rate of $1.29 per $100 of assessed value, the owner of a home valued at $70.000, the county average, would pay about $945 in real estate taxes. Last year the same house would have been assessed at $65.000 and would have cost $947 in county taxes.

The county budget, which takes effect July 1, also includes a 20 cent cut in the vehicle tax rate -- previously highest in the state -- to $5.70 per $100 of assessed value. Under the new rate, the owner of a car valued at $4.000 would save $8 in county taxes over the 1978 tax rate.

Much of the board's often acrimonious two-hour debate, which preceded adoption of the budget, centered on the size of employe pay raises.

County Manager W. Vernon Ford, who submitted a budget $4 million lower than the one adopted by the board, recommended that employes receive a 6.5 percent pay raise. Several weeks ago, most board members tentatively agreed to support Ford's recommendation.

The board adopted a suggestion by Board Chairman Dorothy T. Grotos that gives the 1,500 employes who earn less than $15,600 per year a special one-time payment of $276 in addition to the 5.5 percent raise.

"Infiation continues year after year, and I don't think we're helping our employes when we say we'll give you this one year," said board member Ellen M. Bozman, who attacked Grotos' proposal as "unfair."

Grote disagreed, looking directly at Ford, who she recently criticized as uncooperative with the board's Republican majority. "The easy thing is to take the manager's recommendation and forget it," she said. The $276 payment "is a small token, but at least it's something."

None of the leaders of Arlingionn's employe groups was present at yesterday's meeting. "I don't think anyone's upset," said an employe yesterday, "because we'll be getting the same amount that federal employes are geting."

In addition to the tax cuts, which were made possible by a $7.5 million revenue surplus, the board allocated $39.1 million -- nearly $1 million more than originally planned to operate the county's school system.

At the request of county board member Stephen H. Detwiler, the board lifted a selective hiring freeze imposed six months ago in an attempt to limit county spending. "I think it's appropriate now to let the manager make his own determinations about hiring.' Detwiler said after the meeting. "Of course, we can always impose it again later."

The budget includes several modest additions in county programs as well as an $8 million allocation to pay for Metro transit operations, up 20 percent over last year's budget.

The $166.8 million budget is financed by $31 million in state and federal funds and the rest from Arlington taxpayers, including about $58 million in revenue from the county property tax.