The form itself doesn't offer multiple choices, but the rules for filling it out did, even in '61. Here's the form, this one is a certified copy of one from '63 made circa 1998, but the '61 form, a copy made in 1966, below it is the same, but a bit harder to read.
The field in question, father's race is block 9. Mother's race is block 14.
The one below was created at most a few days after BO's would have been. The posted COLB shows his being filed 3 days before that one, although the births were in the same hospital (Maybe, supposedly, who knows?) and only about 19 hours apart. The file number shown on BHO's COLB is nonetheless 4 numbers higher, rather than somewhat lower as one would expect, but only 3 higher than that of her twin, born a few minutes after she was.
The '63 version has been cropped, so as only to show the copy of the original, and not the certification generated when the copy was made.