THE CAPITOL CRIME that has to be solved in Lawrence Meyer's promising first novel is who killed Les Painter - a Washington investigative columnist who bears a rather startling resemblance to Jack Anderson - and then stuffed the body down a manhole in the basement of the Capitol.

Enter Tony Jordan, a reasonably intrepid reporter who works for a Washington newspaper that bears a rather startling resemblance to the Washington Post. It's Jordan's not unwarranted conclusion that no one really gives much of a damn who killed Painter - not the police, certainly not his fellow journalists (a realistically unsavory lot), and certainly not a handful of highly placed suspects who seem to breathe a collective sigh of relief when the columnist is no more.

Working without any discernible encouragement (especially from his irascible, well-drawn managing editor) Jordan goes after the story. Unfortunately, the columnist's wife has burned all of his files, which probably would have given a clue to the story that her husband was working on - a story so gamey that it got him killed.

Now that Washington has become the crime capital of the free world; the city itself usually assumes the role of major character in the better novels that are written about it. Meyer knows his Washington, is apparently fascinated by it in an engagingly cynical way, and draws it with crisp, bold strokes. Particularly good are his observations about the Senate and its press gallery and his rather witty commentary on the endemic paranoia that seems to grip all newspaper city rooms.

During his quest for the story, Jordan - our reporter as hero - encounters the usual merry band of Washington operators: shifty senators, venal lobbyists, refreshing competent bureaucrats, and overpriced lawyers. It would be difficult, probably impossible, to write a realistic novel about Washington without including an overpriced lawyer or two.

Along the way the reader is also given a course in the methodology of the repoter's grubby trade and here Meyer is especially good. However, he seems a bit uncomfortable, or perhaps bored, when his hero becomes enamored of a beautiful Senator from Nevada. The ho-hum sex scenes appear to be more obligatory than erotic, but since they don't get in the way of the story any serious objection to them would be mere cavilling.

Meyer has developed a sure, almost chilly style which is particularly suited for the suspense novel. His dialogue has a gritty ring to it and is, in spots, quite witty. He has made sure, which is the craftsman's touch, that not all of his characters speak alike.

Although the seasoned readers might decide far, far beyond the end who the villain is, author meyer cleverly keeps pointing his finger at first this suspect and then the other, poroducing enough bafflement in the process to satisfy even the most demanding. The climax, which takes ppalce at a national convention, is a well-done rouser.

Meyer has succeeded admirably in what he apparently set out ot do: write a lean, well-told suspense story about Washington and at the same time take a hard look at those who run this country - or would like to. Along the way he gets in several incisive licks that are well worth pondering.