When the 28-year-old secretary moved from Alexandria to Arlington three months ago, the move caused her and her 2-year-old son Tony unexpected anguish.

Arlington, despite its reputation for being sympathetic to refugees, refuses to give the woman, an illegal alien from Bolivia, any money for day-care expenses. And, with take-home pay of $169 a week, that means she is hard pressed to afford the $40 a week in baby-sitting costs.

Had she moved anywhere else in the metropolitan area, she would have found a local government willing to help pay for her child's day care.

"I haven't asked for help for myself, but for my child," said the woman through an interpreter. "He is a U.S. citizen and I understand he has a right to it." Her son was burned recently when she had to take him to the dry cleaning firm where she works, because she couldn't afford his day care.

Members of the Arlington County Board, who said that they learned of the policy only recently, expressed strong reservations about it and said that they want it reexamined.

"The primary concern is for the child, who is the innocent in all this," said Board Chairman John G. Milliken.

"No one wants to see children neglected or abused," said board member Albert C. Eisenberg. "I'm certainly not interested in a policy whose principal effect is to deprive children of the care they need. If that's what's going on, steps are going to have to be taken."

The Arlington Department of Human Services, which adopted the policy two years ago, maintains that a day-care program is a work-related benefit. Accordingly, department director Martin P. Wasserman argues, illegal aliens cannot enroll their children in the local program because they are not supposed to work.

"It's not like the public school system, where educating the child is a primary purpose," Wasserman said. "Here, the primary purpose of the day-care program is to take care of the child so the parents know the child is in a safe environment while they're working or getting job training."

"It's extremely unfair," said Washington attorney Gisela B. Huberman. Her law firm is challenging the Arlington policy at the request of the American Civil Liberties Union.

Huberman contends that the policy violates the children's constitutional right to equal protection under the law, and is "invidious discrimination against an entire class of children, based primarily on budgetary concerns."

Wasserman said that he would not oppose a change, but does not have the funds to implement one unilaterally.

For the next fiscal year, the Arlington County Board has appropriated $527,000 to take care of 195 children in local day-care programs. In addition, the county is putting up $13,000 as its share of $132,000 in federally sponsored day-care services.

Department estimates show that if the county cared for the children of illegal aliens there would be a maximum of 70 children eligible for the program, said Lynda Eubank, Wasserman's deputy for social services. The change would cost about $100,000 in the first year and double that in subsequent years, she said.

Representatives of local agencies that provide services to aliens, almost all of whom are of Hispanic descent, said they estimate that no more than 30 children would participate in the Arlington day-care program.

"We don't think we're talking about so many children," said Enid Gonzalez-Aleman, executive director of El Rescate Nova (The New Rescue), an Arlington-based agency that provides services to Northern Virginia Hispanics, many of them undocumented workers afraid to go to the county for help.

Marta Wyatt, coordinator of Hispanic social services for the Catholic Charities of the Arlington Diocese, said that there is a "serious problem" with alien parents leaving their children at home alone.

Orlando Mayorga, executive director of the Spanish-Speaking Committee of Virginia, agreed: "Kids are being left at home because they don't have anyone to take care of them, or have the money to get people to come to their houses."

"We call them 'the untouchables' because no one can help them, basically," Mayorga added.