The Arlington County Board voted yesterday to cut both the real estate taxes, in an action that should slighty lower taxes on automobiles and most residences despite rising assessments.

Under the new real estate tax rate of $1.29 per $100 of assessed value, the owner of a home valued at $73,000 - near the county average - would pay about $945 in real estate taxes. Last year the same house would have been assessed at $65,000 and its owner would have faced a county tax of $947.

Republican-backed independents who won control of the five-member board in November had promised to cut the real estate tax rate to offset the county's 13 percent rise in assessments.

"This is a major political victory," Board Vice Chairman Walter L. Frankland Jr. told his colleagues.

"We're delivering on a major campaign promise which affects the pocketbook of every taxpayer. It's a tribute to this board and I don't want to see it buried in tomorrow morning's newspaper."

The unanimous decision to cut the real estate tax rate, which will be reflected in bills mailed to residents in May, was made possible by a $7.5 million surplus that resulted from a higher-than-projected rise in assessments.

County budget officials told the board that cutting the rate 16 cents would cost $5.4 million, leaving more than $2 million of the surplus. The board decided yesterday that part of that money would be used to cut the county's tax on motor vehicles and boats.

The board voted to cut the current personal property rate of $5.90 per $100 assessed value-the highest rate in the state-by 10 cents and indicated that a further reduction is likely next month when the budget is given final approval.

The 10 cent reduction in the personal property tax rate approved yesterday will mean that the owner of a $5,000 car would save $5 in taxes, budget officials said.

In other action, the board voted to require detailed monthly reports from county staff members on the 1,800-unit Buckingham Apartments, Arlington's major moderate-cost garden apartment complex.

Arlington officials and tenants at the 40-year-old, red brick complex, located a half-mile north of Rte. 50 on N. Glebe Road, have complained that the massive project has deteriorated to a "deplorable condition." The project was purchased last year by an Ohio real estate developer who promised he would improve the complex.

"It seems as though the management has directed its attention to a major maintenance program," said community affairs dircetor William L. Hughes. "We intend to ride herd pretty hard to see that the units are safe to occupy."

However, when board member Ellen M. Bozman proposed that the board require monthly reports on improvements, Frankland objected strenuously.

"We ought to let nature take its course," said Frankland, noting that Buckingham officials have promised to clean up the sprawling complex. "If we get into the position of trying to solve the problems of Buckingham, there's nothing to save us from getting into the same thing at other apartment complexes. We don't have time for that."

Despite Frankland's objections, the board agreed to request monthly reports on the condition of the apartment project.