ONE HESITATES to ask, in this age of hearty Republican self- confidence, but the neurotics that Sandy Dennis plays on the screen -- from the hysterical young college professor's wife that won her an Oscar in "Who's Afraid of Virginia Woolf" to the rather strange and older wife of an insurance salesman in "The Four Seasons" -- do they tend in any way to resemble the actress herself?

No, says Sandy Dennis. "You do one thing and that's what people tend to remember you for. But I don't think I am neurotic," she says, in her fluttery breathless voice. And then she tells you about the cats.

Lots of cats, actually. And dogs. Lots of them, too. She finds these strays, and has them fixed and then brings them home and showers them with love. She won't say exactly how many she has, since she doesn't want to claim the attention of the folks who write her letters saying, "Why don't you do things for people and children, instead of a bunch of animals", Either that, or they leave their own unwanted pets on her doorstep in Connecticut, assuming she'll take care of them.

And then there is this to consider about Sandy Dennis: "I like to clean," she says. "Sometimes, I get up at 5:30 in the morning and the first thing I think is, 'What can I clean today.' And then I clean until 10:30 at night, when I fall into bed. It gives me tremendous pleaqsure. I use a toothbrush to clean the baseboards. And I love to watch the shine come up when I buff the floors. I love to have my curtains cleaned and my linens ironed. I love to wash walls." She smiles, her uncertain, somewhat fearful, darting smile. "It's madness."

Well not madness, exactly, but right up there on the eccentricity charts, the Dennis way of confronting the universe being somewhat aligned to the fine old English tradition of living true to a vision at right angles to the geometry of the times. Until recently, when her mother came to live with her, she lived alone, in what used to be the maid's room of her rented house, a room too hot in summer, too cold in winter, but radiating security. In her past, there is no long trail of broken marriages and spiteful romances that seem to be built into a life lived at least partially in the public eye.

"I've never married," she says."It never seemed a reasonable situation. The nicest thing in the world would be to find someone you could talk to, but I guess it's something I never thought about. I never wanted a family. Maybe it's too late. Maybe it's too early. I suppose there's somebody floating out there, but I've always been happy living alone."

She is elusive, kinetic; the molecules of her personality seem set in perpetual motion. There is a kind of erratic, elusive quirkiness to her movements, as if she had thought better of each gesture just after she had let it go. Her sentences, too, break off and begin again in staccato rhythm, as if she were constantly remembering that she forgot something. Her brown hair flies about her shoulders, her dress is more functional than fanciful, and she manages to seem somehow solid and ethereal at the same time.

Dennis is in town to perform in "The Supporting Cast," a comedy that opens at the Kennedy Center tomorrow. Her character, a congressman's wife, "has a few screws loose," she says. "I think she's a little bit mad."

Dennis performs in plays almost exclusively now, Alan Alda's recently released "The Four Seasons" being something of an exception to the rule. "i'm really not a movie actress," she says. "I'm not all that entertainign. I really wasn't that much in demand." Besides, she says, the theater suits her. "I like the life."

She seems to react with wry philosophy to the way the critical winds have blown throughout her career, ever since she left Nebraska at the age of 19 to find her way on Broadway. She first caught the attention of the critics in "A Thousand Clowns" and "Any Wednesday," and it was for her performance in the latter play that the critics went into paroxysms and wrote things like, "Let me tell you about Sandy Dennis. There should be one in every home . . . . The girl is enchanting." That was the good news; at other times, in other plays, the reviews were different. "Miss Dennis plays her part like an ape looking for a banana," huffed one London critic about her performance in a production of "The Three Sisters" directed by Lee Strasberg. She didn't see that review until a year after it was written. "Thank God," says Dennis.

Dennis is 44, a fact she throws in without the usual requisite coyness. "You don't really get to be grown up until you're 40," she says. "What do I mean by that? Oh God, I don't know, why did I say it? I guess it's that you understand that you're not going to live forever. I don't mind getting older. Nothing happened to me until I was 37. And then something nice took place. I guess the really important thing is I learned to work for myself, and to get more enjoyment out of it than when I was young and desperate and wanting knowledge."

And no, she says, she isn't particularly sorry that she didn't glean a larger measure of fame in her life. "It would have been wonderful financially, of course, and I would have handled it so well. But I think I had just enough," And what of her life these days?

"It's up and down," she says, as she gets ready to go to rehearsal. "Right now, it's good. I feel lucky to be alive; so many things please me." And even in her darker days, she says, she doesn't forget that it is a fortunate thing to be living. "I just think, 'What would all those cats do without me?'"