I have gone through the university's website. Their website does mention anything about this.
I couldn't find anything mentioning enrollment criteria for the University of Cape Town during the apartheid era.
From a review of the book, The University of Cape Town: Between apartheid and academic freedom
In the wider context of apartheid South Africa, the University’s reputation as the most liberal institution (next to Wits) was well deserved, but this also shows what little space the regime left for academic and civic freedom.
The first intake of black students was in the 1920s. The numbers remained low until the 1980s and 1990s.
For its sustained opposition to apartheid from the 1960s to the 1990s, the university earned the name "Moscow on the Hill".
The initial hopes of more liberal-minded academics of creating an environment that was more responsive to the educational needs of students from the majority of the South African people, including those classified as coloureds, Indians and Asians, were shattered when the relations between the University management and the government became progressively tense in the 1960s.
While the numbers of coloured and Indian students, who constituted the majority of ‘non-white’ students, increased from 2.98% in 1948 to 12.4% by 1959, this section of the student population dwindled to a mere 5.5% by 1968 as a result of the intensifying enforced separation between black and white.
despite the University’s attempts to exploit grey areas and loopholes, its ‘timid brand of liberalism’, which often glossed over the many instances of segregation in and outside lecture halls, does not lend itself to heroic tales of principled white liberal resistance
There were no specific tests. The requirements were the same as for whites. It's a common misconception that blacks and coloureds couldn't go to white universities. However they could get special permission provided they were gifted enough and there was no black university offering the same main subject.