Sen. Alfonse M. D'Amato (R-N.Y.), chairman of the Senate Appropriations Subcommittee on the District of Columbia, was confronted with a small dilemma last week. At public hearings on the city's 1982 budget, antiabortionists made their annual plea for a budget rider outlawing the use of city money for abortions.

Since D'Amato took over the subcommittee, he has prided himself on being a friend of local home rule who doesn't interfere in city affairs. But on the other hand, he is a staunch anti-abortionist who owes a lot to the right-to-life lobby.

To the astonishment of many pro-choice advcates who were braced for the worst, D'Amato sided with the District, saying, "I will continue to be outspoken for the human life amendment," but added that for District officials to provide city-funded abortions "is their particular choice and right. I have great reservations on interference in this area."

"I went over there expecting to be blown away," said Leslie Harris, executive director of the local chapter of the American Civil Liberties Union and a member of the pro-choice D.C. Abortion Rights Coalition. "This was the prototype situation for testing out how he's going to stand on home rule. Though he and I are ideologically different on most issues, I was impressed."

To the surprise of many who feared what the conservative D'Amato might do, over the last five months D'Amato consistently has come down on the side of the mayor -- even if that meant offending other quarters of the government, like the school board.

D'Amato has, in fact, started his tenure as chairman where his predecessor, Sen. Patrick Leahy (D-Vt.) left off. Leahy started by involving himself in decisions on the Washington Convention Center and the ill-fated second campus for the University of the District of Columbia. But Leahy eventually became a more vocal advocate of home rule and scrapped the traditional line-by-line review of city budgets.

About the only time D'Amato became openly involved in a city issue was when he wrote a letter of endorsement urging Mayor Marion Barry to appoint Assistant Police Chief Charles E. Rinaldi as the city's new police chief. Barry declined, appointing instead Maurice Turner. D'Amato's aides have insisted that the whole episode was blown out of proportion.

As the months go on, D'Amato's philosophy on the subcommittee has come into sharper focus and can be summed up as: Give the mayor what he wants, then hold him accountable if the city can't get its act together.

"He doesn't wield a bit stick," said an aide to D'Amato. "He's saying, "Here's your choice, do it.' If the city now doesn't live up to that responsibility, we'll see what he (D'Amato) will do then."

One recent example of D'Amato's philosophy at work came when Barry ventured up to Capitol Hill and D'Amato told him there wasn't enough money allotted in the 1982 budget for the city's pension fund. Barry insisted that maintaining the pension fund was the responsibility of the federal government, not the city, and that he had taken that position on the advice of the attorney for the Retirement Board.

D'Amato, who could have easily shifted a few million dollars here or there to swell the pension fund, told Barry in essence: Fine. Put that in writing, and I'll hold you to it. In other words, if that's your prosition, don't come back here later and ask for money.

That tactic is far removed from the ones used by old-time senators who pored line by line over each item in the city's budget. It is also far removed from the visions city officials once had of D'Amato as an obscure, dogmatic town hall crony from Long Island who catered to the most conservative instincts of a white, blue-collar constituency.

Their other fear was that D'Amato, coming from a job as presiding stipervisor of the Town of Hempstead, population nearly 800,000, may have had the notion that he knew all about how to run a city of about 638,000. Quite the contrary, his aide said. Schooled in the problems of federal interference in local government, D'Amato has little desire to interfere in District affairs.

"One of the things that he ran on was the fact that the federal government overregulated some of the local governments," said the D'Amato aide. "Now he is part of the federal government and his job is to regulate a local government. He has an understanding of the needs of local governments."