An insistent group of Takoma Park residents last week approached a visiting panel of state delegates and asked that they change the Montgomery-Prince George's county border that cuts the city in two. They said it tangles everything from taxes to home improvements.

The appeals brought waves of applause as speakers at the municipal center pushed for a law that would place all of Takoma Park in Montgomery County. Throughout the city's 99-year history its southeast third has been part of Prince George's County.

City officials are trying to arrange an advisory referendum on the unification issue, a straw vote to be taken Nov. 2 at the city's six polling places. City residents would be asked if they want county boundaries changed so that the entire city is in Montgomery. Their responses would be sent to the legislature in a new drive by city officials to change the county border.

A bill calling for an official referendum on the unification question was killed April 8 when Prince George's delegates opposed it.

In trying to set up the advisory referendum on uniting the city, Mayor Sammie A. Abbott last week had to send his appeal to election officials in both counties.

Officials say that hashing out such arrangements with two governments has ensnarled business over the years for city administrators and for residents on the border who sometimes get the runaround from both jurisdictions.

Nine delegates and legislative candidates sat at the City Council table and listened to a litany of bureaucratic headaches caused by the split jurisdiction.

"If you look at the map in front of you," Gail B. Dalmat said as the representatives dutifully shuffled papers, "you'll see that the county border runs right through my house."

Dalmat, who lives at Elm and Poplar avenues, said she once needed service on her water line. She called officials at the Washington Suburban Sanitary Commission. They advised her to contact Montgomery officials, who advised her to talk to Prince George's officials, who advised her to call the city. Eventually, she said, the sanitary commission provided the service.

"It's sad, in a way," said Patrick A. Donnelly, a resident of the Prince George's section by a margin of several feet. "Children grow up together to live together. Children in one house go to P.G. schools and their friends next door go to Montgomery County."

Other residents criticized Prince George's County officials for spending less per pupil than other county school systems in the metropolitan area.

One witness said she had trouble getting Silver Spring taxis for guests visiting her home on the Prince George's side; another had trouble persuading a contractor to build a backyard fence that would require driving to Upper Marlboro for a building permit.

Abbott said that Prince George's County is stingy with the property tax revenue it returns to Takoma Park for police, library and other services the city provides itself through its own property tax. He noted that Montgomery boosted its revenue return to the city last year.

Most of the elected officials at the city meeting listened quietly, occasionally commenting on the legislative and logistical problems involved in transferring the area into Montgomery.

Sen. Arthur Dorman (D-P.G.) said he and other officials would look into the mechanics involved, and promised, "We will keep you informed . . . ."