Dorothy T. Grotos, one of two Republicans on the Arlington County Board, said yesterday that she will run for county treasurer rather than seek a third term on the board.

The other Republican on the board, Walter L. Frankland Jr., who has been Grotos' running mate in their past two campaigns, announced last night that he will seek reelection.

Grotos made her announcement at a news conference at which Treasurer Bennie L. Fletcher Jr., also a Republican, said he will retire after 29 years in the treasurer's office, the last dozen as its head.

The treasurer has 49 employes and is responsible for mailing out all county tax bills, collecting all revenue and paying all bills. The starting yearly salary is $41,564, compared with the $10,206 paid for county board membership, which is considered a part-time job.

Grotos, 52, said yesterday that she likes "the public service aspect of the treasurer's job." She said "everything on the county board today is so political. It's nights, weekends. I'm away from my family a lot and we the board seem to be spending a lot of time and accomplishing little, like this budget review process. We're not making any decisions. I might as well be out fishing or home polishing the floor."

Grotos and Frankland have run for the board as independents with Republican endorsement rather than as their party's nominees, to encourage participation in their campaigns by federal employes who are barred by the Hatch Act from participating in partisan political campaigns.

Frankland is expected to win the GOP endorsement handily at the county Republican canvass May 17. Arlington School Board member Michael E. Brunner said Monday he will seek GOP endorsement for his independent candidacy for the board, and John Marshall, a senior manager with the U. S. Department of Education, is expected to make a similar announcement soon.

Grotos is the favorite for the GOP treasurer endorsement. William Nehrke, a program officer for the Navy Supply Systems Command, said last night that he will also seek the party's endorsement for the job.

Grotos and Frankland, proven vote-getters, form the minority on the five-member board now controlled by Democrats. The Republicans controlled the board for four years until Stephen H. Detwiler lost his reelection bid to Democrat Mary Margaret Whipple last fall.

Since then, Grotos and Frankland have been under pressure to run again to avoid a complete takeover by the Democrats, who have won the last three board elections. Both are considered moderate-conservatives in a county that has voted for moderates to liberals in recent years.

"I don't know whether it the Democrats' victory is a trend or if the people running are just able to sway enough votes," said Frankland, 59, executive vice president of the Silver Users Association.

"I've seen the current majority in operation and it bothers me, seriously concerns me," he continued. "We have to have our voices heard there. We need a strong two-member team which will assure our voice is heard."

Republican leaders were expecting Grotos' decision, which she said she delayed until Fletcher was ready to announce his retirement.

But County Board Chairman Ellen M. Bozman, a Democrat-backed independent, said she was surprised. "I've heard all the rumors," she said. "But if I had laid down my money, I would have said she would run for the board and Walter would retire. She likes setting policy so I'm surprised she would give up the making of county policy for a fiduciary job."

As treasurer, an office created by the state constitution, Grotos said, she would be independent from the board. She nodded in agreement with Fletcher's assessment that neither the board nor the county manager "can dictate to the treasurer."

A champion of parks and recreation programs and assorted neighborhood causes during her eight years on the board, Grotos said she has had administrative experience as director of several summer youth camps. From her County Board work, she said, "I probably know a great deal about the county government, how it operates, how the budget works."

Grotos is expected to face Democrat Frank O'Leary, president of Nova Research Associates, for the treasurer's post.

At a meeting of the Arlington Republican Central Committee last night, Arlington Commonwealth's Attorney Henry Hudson said he will once more seek GOP endorsement for reelection and Helen Blackwell, a self-described conservative, was elected to a one-year term as the committee's chairman. Blackwell succeeds Jade West, another conservative who announced plans to resign last month.

Blackwell, a newsletter writer for the Eagle Forum, a New Right political organization, is a 10-year member of the committee and served as its chairman in 1975.