TWO WEEKS AGO, freshman Sen. Alfonse D'Amato (R-N.Y.) sent a letter to Mayor Barry endorsing one candidate in the jockeying that went on to become the city's next police chief.The letter immediately set off criticism around town because it touched on two sensitive matters. The senator endorsed the only white candidate for the job. And his letter also angered people who have been fighting for the idea that, though this may be the nation's capital, the citizens who live here are entilted to govern themselves. In a phrase, they -- we -- have a right to "home rule."

As a newcomer to the city and newly appointed head of the Senate D.C. appropriations subcommittee, Mr. D'Amato may not have realized exactly what he waded into. In the 10 years that have passed since Congress ran the city, people have been very vocal about their right to elect a mayor, a city council and a school board and to vote for president. What is less apparent is that many people, including some ostensible supporters of home rule, also like the idea that Congress has some say in local affairs. They especially like having a friend in Congress when things are not going their way in the District Building.

The most recent example of this double approach occurred in last year's gambling initiative vote. After the initiative had won public approval, a group of local ministers and politicans who had opposed it went to the Hill seeking to get Congress to overturn the bill before it became law.

Now into the D.C. political scramble comes Sen. D'Amato. Some people will surely approach him to ask that he make a call, write a note or deliver this message or that on the way the city should be run. What such people never say is that if the senator -- or any other "helper" -- ever opposes them on any issue they will holler up a storm about congressional interference in city affairs. The best the senator could do is to stay out of these strictly local fights. There are enough problems with the city budget and his committee has some real responsibility for helping with those. But aside from that, the ideal posture for any senator in dealing with the city government is: hands off.