CHICAGO. Jan. 27. After a month of Chicago rehearsals to which the public was invited, Tennessee Williams and "The Rose Tattoo" go to New York's Martin Beck Theater Saturday for the verdict of the critics.

To suggest that Mr. Williams is concerned about critical appraisal of his new play is understatement. 'If the critics don't like what I do," he states flatly, "I can't expect the public to like what I do."

That is why "The Rose Tattoo," like "The Glass Menagerie" before it, opened in Chicago and not on Broadway. There are drama critics here, Mr. Williams says, who are willing to devote considerable attention to his last-minute polishing. As a result, the author believes that the play unveiled in New York will be greatly improved. .

Mr. Williams was on hand for most of his new play's run here at the Erlanger Theater. Except for a few days in New York, he was at the theater at noon every day for rehearsals. Nor did he miss the evening performances to which the paying customers flocked in satisfying numbers.

Working closely with the director Daniel Mann, he saw the sun rise from Lake Michigan almost daily as he labored to quicken the play's pace and to make every line incisive.

"I never worked harder on a play," says Mr. Williams, "arid I never did so much rewriting. I found this the most difficult play of any I wrote because of the delicate balance of humor and tragedy."

"The Rose Tattoo" is indeed a tragie comedy. It is the story of Serafina Delle Rose, who lives in a village of Sicilians "somewhere along the Gulf Coast between New Orleans and Mobile." Serafina, a warm-blooded woman of thirty, is widowed when her husband is killed transporting a cargo of narcotics under a truckload or bananas.

For three years the badge of her widowhood is her unkempt dress. Serafina divorces herself from the realities of living although she supports her beautiful fifteenyear-old daughter, Rosa, with her sewing machine.

Serafina refuses to consider taking a substitute for the handsome and romantic husband, a "baron" in Sicily, whose ashes she treasures. Wistfully, she recalls the red rose that was tattooed on his chest and the red rose stigmata that once, for a moment, was mirrored on her chest. Her daughter, too, must lead a cloistered existence until Serafina can find her a husband with the dead man's qualities.

The arrival of Alvaro Mangiacavallo (Sicilian for "eat a horse") changes Serafina's life. she joy ously embraces Alvaro, who hae her husband's "beautiful body and the face of a clown," after learning of her late husband's infidelity. Serafina smashes the urn holding her husband's ashes when a woman gambling house employee admits a rose is tattooed on her chest, placed there during her romance with the late "baron."

Serafina can now face life joyously and forget the ashes that were carried away by the wind when the urn was smashed. Her daughter, a witness to her passionate discovery of Alvaro, is permitted to meet a sailor-lover in New Orleans.

Mr. Williams began writing "The Rose Tattoo" in Rome exactly a year ago. He says the play was directly inspired by the "vitality, humanity and love of life expressed by the Italian people."

"The mystery of the Dionysian quality," the author says. "is the play's theme. It shows through Serafina that instead of living on romantic terms people must live on ordinary terms."

"The Rose Tattoo" is the happiest play yet to come from Mr. Williams' typewriter. "I have felt more hopeful about human nature as a result of being exposed to the Italians," Mr. Williams explains. "And I have been much happier in the last two or three years than ever in my life."

In "A Streetcar Named Desire," the playwright says. the central character. Blanche, is "negative and pitiable." He feels Seraflna is "positive and admirable."

"The Glass Menagerie," he says, "is a statement of the human situation and nothing is resolved.,

In "The Rose Tattoo" he sees "the same basic human situation with a positive solution in which a woman discovers she can meet life on its own terms and be fulfilled." .

Mr. Williams confesses he had Anna Magnani, the Italian film star, in mind for the role of Serafino. "But it took me many weary months even to arrange a meeting with her." Mr. Williams says.

"I saw her at long last in August and quickly put her out of mind. Her demands were exorbitant. She demanded control of " every aspect of the play. she would not agree to appear for more than four months÷and then not until late in 1951. She wanted much money that we would have to run for two years just to pay her salary."

Miss Maureen Stapleton makes a much better Seraflno, declares Mr. Williams, who is enthusiastically seconded in this by director Mann. It is their opinion that Miss Stapleton, who played opposite Melvyn Douglas in "The Bird Cage," is more convincing in the passionate and mature role than the Italian star could be. They also, are greatly satisfied with Eli Wallach, a young Broadway veteran, as Alvaro.

"It is my hope that the public will like them and the play," Mr. Williams confides. "It is a romantic play that will appeal to romantic people."