THERESA FORTUNATO, the heroine of Kate Green's very accomplished first mystery, Shattered Moon (Dell, paperback $3.95), is a practicing psychic, and it is her clairvoyant "gift" that involves her in the police hunt for a psychotic killer. Desperately longing to banish the visions which pull her, with such excruciating vividness, into the world of murderer and victim, she wishes only to be left in peace, doing "graceful and loving" Tarot readings for people who come to her with the ordinary run of human problems.

But, of course, that's not the stuff of suspense. However, the way Green makes us feel the reality of Theresa's internal conflict about her paranormal abilities certainly creates a tension all its own, and this works to deepen the shocks of the steadily occurring violence.

"I expected a craggy old gypsy with a turban and a crystal ball or a crone with a pointed hat," a new client nervously confesses, as the novel opens. She's come to consult Theresa about her missing daughter, and, what the horrified Theresa sees -- "and "experiences" -- is the unfortunate girl's grisly death.

As more corpses turn up, Theresa finds herself unable to tune out those flashes that reveal to her the victim's last moments, but what she cannot see, until it's nearly too late, is the identity of the killer.

Even skeptics would acknowledge, I think, how naturally Green sets up the situation: one simply accepts Theresa's special powers and the relationships they affect, with Michael, her ex-husband, with Los Angeles cop Oliver Jardine, with Neal Holton, the undercover detective assigned to watch her, and with the mysterious deranged man who's carefully planning her death. Give Me Rewrite!

JUST AS Theresa Fortunato is the latest in a rather long line of psychic sleuths, so is Lucy Shannon a character with plenty of genre ancestors. A wisecracking girl reporter for the fictional New York Blade, she makes her bow in One for the Money (Academy Chicago, $14.95), which is New York Post city editor Dick Belsky's debut, too. But unlike Theresa, Lucy's eager to play Sherlock.

"As murders go, this sounded like a pretty good one," she thinks to herself as she heads toward the scene of the crime. "The victim was probably attractive. A career girl. Upper East Side. It was the kind of thing that pushes all those boring stories about Ronald Reagan and disarmament talks off the front page and back to page 58, next to the crossword puzzle."

Since the Blade is a tabloid that needs daily fresh sensations the way a vampire needs transfusions, Lucy blissfully contemplates media stardom when she keeps stumbling across new bodies that assure her of front- page bylines. Three exclusives, and she's being introduced around at Elaine's.

But the formula demands that even the hard-boiled Ms. Shannon act just a little like a damsel-in-distress. Even so, she remains game after getting punched around a bit by the Mob, nearly run down by a speeding car and even after confronting the wrong end of a .38. This is a fast and funny whodunit that would make a dandy pilot for a television series. Parties of the First Part

HAUGHTON MURPHY's Murder for Lunch (Simon and Schuster, $14.95) and Donald Lehmkuhl's The Woman in the Moon (Doubleday, $12.95) are two more first mysteries worth a prolonged stay in an armchair.

In the former, Murphy, a pseudonymous Manhattan lawyer (rumor has him a partner at Cravath, Swain and Moore) obviously enjoyed himself while concocting this wry look at the office politics of a big, successful firm. In the latter book, the author's pleasure is equally apparent as he takes bitchy aim at British feminist journalists, talentless rock musicians and New York magazine editors to name just a few of his targets.

In Murder for Lunch, the detective is Reuben Frost, semi-retired but still as interested in the goings-on at Chase & Ward as when he'd embarked on his distinguished career there way back in 1935. After Graham Donovan, the likely successor to the current executive partner, collapses, poisoned, while at lunch with his senior colleagues, Frost happily finds himself useful once again.

His methods of investigation are cautious but sure, as befits an elderly wall Street veteran: it's only this sudden death at his doorstep, so to speak, that holds any surprise value. To deal with the rest of the things he uncovers in the process of finding the killer, from illicit affairs to insider trading, is merely a matter of arranging matters so that the honor of Chase & Ward is preserved.

Zena Baird, the slightly haggard queen bee of The Woman in the Moon, is an advice columnist who turns detective when one of her correspondents gets herself murdered on the common outside Zena's house. Fortyish and feeling it, Zena has to keep slogging away at her writing for Eve, "The Magazine for the Woman Who Won't Take It Lying Down," because her husband, Simon, is an "outstanding failure" in his chosen career as a pop guitarist.

Those not in the least interested in London's lesbian subculture should probably avoid this novel. Even if Zena's decidedly heterosexual, very few, if any, of the other female characters are, and just about everyone the plot winds around is leading a fairly sleazy life.

Agatha Christie's England it's not but Lehmkuhl, veering between dashes of satiric wit and sledgehammer blows of sheer malice, has recreated a milieu that exists -- even if the Zenas of this word are no more likely than the Miss Marples to run across so many dead bodies. Cooking the Books

LAWRENCE BLOCK, whose sixth Matt Scudder mystery When the Scred Ginmill Closes (Arbor House, $15.95) this is, wrote his first book in 1961. Scudder is an ex-cop, now an unlicensed private investigator, who likes to shoot the breeze with cronies and not avoid trouble when it comes along, particularly if it's a matter of helping a friend.

Who held up Morrissey's, a Hell's Kitchen after-hours joint, on the Fourth of July, 1975? Why is the undoctored set of account books missing from Armstrong's, Scudder's favorite bar? Why did Tommy Tillary's wife, Margaret, get stabbed to death in Bay Ridge?

Although Block is a very competent writer and an intelligent observer of human types, it takes three-quarters of the book's length for this story to get going and make any sense. There's a pretty chilling finish, which for some will make the slow going worth it, but it really is too little, too late, even if all three crimes are neatly tied together and avenged.