The Arlington County Board yesterday passed a fiscal 1977 budget that calls for a slight decrease in the county's property tax rule, but not enough to make up for the higher taxes residents will pay because their assessments have gone up.

The Board set the tax rate at $1.49 for each $100 of assessed value, when homes are assessed at their full market value. This is a decrease of 2.2 cents from the rate Arlingtonians paid last year. The new rate is the second lowest if the Washington metropolitan area after Loudoun County.

"The same thing could be said about it was said for a similar cut in taxes in Alexandria - that it is a token," said Board member Ellen Bozman.

Even so, Bozman said she thought the tax cut "could be helpful." For homeowners, whose average assessment increased 6 per cent this year, the tax cut would mean a savings of slightly more than $13 a year on a $60.000 home, which is close to the county's average home value, according to county budget officials.

The new rate which must be formally ratified following a June 25 public hearing, would stay in effect at least until May, 1978. Board members indicated. "We don't want it to be a yo-yo, going down and then right back up," said Board Chairman Joseph Wholey.

Bills for the first installment of this year's property taxes, which have already gone out and are due today, reflect the unreduced tax rate of $1.512 for each $100 of assessed value. The next tax bills will be reduced to compensate for what will now be an overpayment of taxes based on the first installment bills. The new rate is 1.5 per cent lower than the current rate.

The Arlington budget for the fiscal year that begins July 1 calls for spending $108.2 million from local funds for county services and construction and $45.3 million for the Arlington public schools.

These figures include money for pay increases ranging from 3 to 5 per cent, for county employees. The County Board also established a $14,000 contigency fund in case it decides later to raise its own member salaries.

The school budget, which requires a county contribution of $35.24 million (with additional funds coming from state and federal sources), allows the School Board to restore services that have been cut during the past few years because of financial difficulties.

It will provide about $508,000 for textbooks and supplies, funds for routine school maintenance, full-time reading specialists and librarians in all but two small elementary schools, remedial skills centers in junior high schools and a small summmer school program, School Board President Diane Henderson said.

The County Board voted the funds after rejecting a motion by Board member Dorothy Grotos to provide only $44 million for schools. Grotos said that while some county services had been cut with a butcher knife, "we did not even use a scalpel on the school budget."

The contigency fund for Board members' salary increases would provide the necessary funding if the Board decides to increase its pay as allowed by state law. The Board could increase pay for members by 50 per cent, raising it from $6,000 to $9,000, and pay for the chairman by 25 per cent, raising it from $8,000 to $10,000. Board members are considered part-time.

The Board voted to increase pay for nonsupervisory professional and technical workers, clerical employees, and nonsupervisory trade and maintenance workers by 4 per cent, effective June 19, 1977. Nonsupervisory police and fire officers were granted a 3 per cent general increase and employees in management jobs were granted two increases, 2 per cent on June 19, and 5 per cent in January, 1978.

County Manager W. Vernon Ford said that in previous years management employees had not received pay increases as large as those for lower level workers.

County employees have complained that they are being shortchanged on wages and benefits as a result of a Virginia Supreme Court ruling that public employees may not bargain collectively.