Midwestern stories of menace, despair; Places in the World a Woman Could Walk, by Janet Kauffman. New York: Alfred A. Knopf. 132 pp. $11.95.

The dozen stories that make up Janet Kauffman's new collection are situated in the small towns and open spaces of south-central Michigan and northwestern Ohio. And, in Kauffman's telling, the people of this region apparently cultivate eccentricity more strenuously than land.

They live in trailers and unfinished or small houses, these people. And they have names like Lady Fretts, Marabelle, Dahlia, Wil-Johnny, Asuncion Smith, Doll Fether, Durango, and Bobby-Boo.

Kauffman's characters are not happy; some of them are tense and scared, like the family in ''How Many Boys?'' This story, which must encompass 30 or so minutes in the lives of its characters, concerns two phone calls, both wrong numbers. It begins:

Before they sat down to supper, the phone rang. The father picked up the phone on his way to his chair.

''Is the boy back from the paper?''

It was a woman's voice - nasal, insistent.

''What?'' said the father. ''One of our boys?''m

After some worry about where the family's boys are, they sit down to a pleasant dinner, after which comes the other call. The mother answers, and hears a small child cry ''Ma!'' four times. Finally the mother says, ''You must hang up the phone now. Just dial the telephone again. I'm hanging up now. Good-bye.''

''How Many Boys?'' continues for only another two pages, but they are haunting pages: Whose child was it? What was wrong? What can they do? What can anyone do? The story is a slice of lonely and fearful life.

Most of the stories in ''Places in the World a Woman Could Walk'' aren't so menacing; instead they are just despairing. Robert, the narrator of ''The Mechanics of Good Times,'' tells us:

''Prattville, I have discovered, is a place you can find . . . a woman . . . who is first of all glad for a trailer. Which is not, I know, a pretty quality. But it is a good indication of this virtue - namely, the lack of wishes. I look for that finally. But I know that wishlessness is not stupidity. To be wishless is to be ready - for me, for instance; for come-what-may. Alice, I'm sure, does not dream of kitchens or pastel knitting.''

Robert is one of two male narrators (10-year-old Bobby-Boo in ''At Odds'' is the other) in this collection. And, while there are men present (or conspicuous by their absence) in Kauffman's stories, they are mostly shadows, insubstantial figures about whom the women often talk and without whom they manage just fine.

Celia Dollop, who left her abusive husband to live by herself in the woods, says, ''I'm down to nothing; it's about time.'' The mother in ''My Mother Has Me Surrounded'' tells her daughter: ''You're lucky to be a girl. Men are really unlucky; they have a hard time just living. Especially the powerful. They don't know what to do with the world, except run it.''

It is tempting to label Kauffman a regional writer, one who, like such short story writers as Bobbie Ann Mason, creates distinctly rural fictional worlds. But that label would be wrong. ''The local is the only universal,'' said William Carlos Williams, and Kauffman's stories illustrate the truth of his remark.