White enrollment in private and parochial schools in the 1960s was closely tied to the racial makeup of the nation's largest cities, and these enrollments often increased in cities with heavily black populations, a Johns Hopkins University study has shown.

Washington topped the list of the cities in the study whose white enrollment in nonpublic schools increased. About 37 percent of Washington's white students were enrolled in these schools in 1960; the figure was 47 percent 10 years later.

The study indicates that tuition tax credits designed to aid parents of private and parochial school students "may result in greater social-class and racial segregation of American children than now exists," according to study director Henry Becker.

Becker said the tax credits might intensify the relationship between race and private school enrollment found in the study. The tax credits, he said, might be "more widely used by white families in cities with large or growing black populations, and could inhibit progress school desegregation in these cities."

A controversial propoosal to establish federal tax credits for private college, secondary or elementary tuition is scheduled to come up in the Senate this week.

Spokesmen, for public schools including Health, Education and Welfare Secretary Joseph A. Cslifano Jr., have warned that providing a tax subsidy for private school tuition would increase the exodus from public schools and seriously hurt many systems.

Blecker noted in his study that the large cities where white enrollment in private and parochial schools increased in the '60s were either southern cities or northern ones with large black populations. These cities included Washington, Atlanta, Miami, Charlotte, Dallas, Fort Worth, Philadelphia, Detroit, Newark and New York.

The 10 percent increase in whites enrolling in non-public schools in Washington between 1960 and 1970 seems "more startling when you rcalize that in most large northern cities the figure was going down between 5 and 10 percent," Becker noted.

He pointed, for instance, to Milwaukee, a city with a few minority population, in 1960 about 36 percent of the white students were enrolled in non-public schools; by the end of the decade the percentage was down to 26, he said.

Washington's experience of increasing white enrollment in parochial and private schools appears to be continuing in the 1970s, according to figures provided by the Division of Research and Evaluation. In October 1977, about 55 percent of the city's "non-black students were attending non-public schools, the figures showed.

The Hopkins study was based on data from the 1960 and 1970 censuses. According to Becker, it was the first statistical look at private school enrollment according to race.

Becker emphasized that the figures do not necessarily reflect what has happened in the 1970s.

Still, the Council for American Private Education found the study "alarming and misleading," according to council executive director, Robert Lamborn.

"The facts since 1970 are substantially different than the facts prior to 1970," said Lamborn, whose organization is an umbrella group for about 90 percent of the nation's private and parochial schools.

"I'm not criticizing the scholarship of this study, but I am worried when a study done by anyone attributes movement to factors that are basically racial," he said.

"A great deal movement from public to private schools has had nothing to do with race. Most of the changes have been attitudinal, reflecting desires of parents to find the best schools possible for their children."